Exam 4: Exponential and Logarithmic Functions

Choose the one alternative that best completes the statement or answers the question. Find the domain of the composite function f ° g. - $f ( x ) = 7 x + 14 ; \quad g ( x ) = x + 7$

(Multiple Choice)

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Question 361

Write the word or phrase that best completes each statement or answers the question. -What principal invested at 6%, compounded continuously for 3 years, will yield $1500? Round the answer to two decimal places.

(Short Answer)

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Question 362

Find the amount that results from the investment. - $\$ 12,000$ invested at $5 \%$ compounded quarterly after a period of 2 years

(Multiple Choice)

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Question 363

Graph the function. - $f ( x ) = e ^ { - x }$ $Graph the function. - f ( x ) = e ^ { - x }$

(Multiple Choice)

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Question 364

Find a formula for the inverse of the function described below. -A size 44 dress in Country C is size 2 in Country D. A function that converts dress sizes in Country C to those in Country D is $f ( x ) = \frac { x } { 2 } - 20$ .

(Multiple Choice)

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Question 365

Find the amount that results from the investment. - $\$ 1,000$ invested at $4 \%$ compounded semiannually after a period of 6 years

(Multiple Choice)

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Question 366

Choose the one alternative that best completes the statement or answers the question. The graph of a logarithmic function is shown. Select the function which matches the graph. -

(Multiple Choice)

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Question 367

Solve the equation. - $\log _ { 3 } ( 3 x + 7 ) = \log _ { 3 } ( 3 x + 2 )$

(Multiple Choice)

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Question 368

Choose the one alternative that best completes the statement or answers the question. - $\ln \frac { ( 6 x ) \sqrt [ 9 ] { 1 + 3 x } } { ( x - 9 ) ^ { 7 } } , \quad x > 9$

(Multiple Choice)

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Question 369

The function f is one-to-one. Find its inverse. - $f ( x ) = \frac { 2 } { x - 4 }$

(Multiple Choice)

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Question 370

Solve the problem. Round your answer to three decimals. -What annual rate of interest is required to double an investment in 10 years?

(Multiple Choice)

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Question 371

Find the exact value of the logarithmic expression. - $\ln \mathrm { e } ^ { 8 }$

(Multiple Choice)

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Question 372

Use transformations to graph the function. - $\text { Use the graph of } \log _ { 4 } x \text { to obtain the graph of } f ( x ) = - \frac { 1 } { 3 } \log _ { 4 } x \text {. }$ $Use transformations to graph the function. - \text { Use the graph of } \log _ { 4 } x \text { to obtain the graph of } f ( x ) = - \frac { 1 } { 3 } \log _ { 4 } x \text {. }$

(Multiple Choice)

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Question 373

Write the word or phrase that best completes each statement or answers the question. Solve the problem. -Determine the domain of the function f(x) $f ( x ) = \log _ { 5 } ( x + 2 )$

(Short Answer)

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Question 374

Use a graphing calculator to solve the equation. Round your answer to two decimal places. - $\log _ { 4 } ( x + 2 ) - \log _ { 5 } ( x - 1 ) = 1$

(Multiple Choice)

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Question 375

Write as the sum and/or difference of logarithms. Express powers as factors. - $\log _ { 3 } \left( \frac { x ^ { 2 } } { y ^ { 6 } } \right)$

(Multiple Choice)

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Question 376

Find functions f and g so that f ° g = H. - $H ( x ) = \frac { 6 } { \sqrt { 9 x + 10 } }$

(Multiple Choice)

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Question 377

For the given functions f and g, find the requested composite function. - $f ( x ) = 5 x + 10 , \quad g ( x ) = 5 x - 1 ; \quad$ Find $( f \circ g ) ( x )$

(Multiple Choice)

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Question 378

The graph of a one-to-one function f is given. Draw the graph of the inverse function f-1 as a dashed line or curve. - $f(x)=2 x$

(Multiple Choice)

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Question 379

For the given functions f and g, find the requested composite function value. - $f ( t ) = \sqrt { t ^ { 4 + 18 t ^ { 2 } + 81 } } , \quad g ( t ) = \frac { t + 3 } { 3 } ; \quad$ Find $( f \circ g ) ( 9 )$ .

(Multiple Choice)

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Question 380

Choose the one alternative that best completes the statement or answers the question. Find the domain of the composite function f ° g. - $f ( x ) = 7 x + 14 ; \quad g ( x ) = x + 7$

Write the word or phrase that best completes each statement or answers the question. -What principal invested at 6%, compounded continuously for 3 years, will yield $1500? Round the answer to two decimal places.

Find the amount that results from the investment. - $\$ 12,000$ invested at $5 \%$ compounded quarterly after a period of 2 years

Graph the function. - $f ( x ) = e ^ { - x }$ $Graph the function. - f ( x ) = e ^ { - x }$

Find a formula for the inverse of the function described below. -A size 44 dress in Country C is size 2 in Country D. A function that converts dress sizes in Country C to those in Country D is $f ( x ) = \frac { x } { 2 } - 20$ .

Find the amount that results from the investment. - $\$ 1,000$ invested at $4 \%$ compounded semiannually after a period of 6 years

Choose the one alternative that best completes the statement or answers the question. The graph of a logarithmic function is shown. Select the function which matches the graph. -

Solve the equation. - $\log _ { 3 } ( 3 x + 7 ) = \log _ { 3 } ( 3 x + 2 )$

Choose the one alternative that best completes the statement or answers the question. - $\ln \frac { ( 6 x ) \sqrt [ 9 ] { 1 + 3 x } } { ( x - 9 ) ^ { 7 } } , \quad x > 9$

The function f is one-to-one. Find its inverse. - $f ( x ) = \frac { 2 } { x - 4 }$

Solve the problem. Round your answer to three decimals. -What annual rate of interest is required to double an investment in 10 years?

Find the exact value of the logarithmic expression. - $\ln \mathrm { e } ^ { 8 }$

Write the word or phrase that best completes each statement or answers the question. Solve the problem. -Determine the domain of the function f(x) $f ( x ) = \log _ { 5 } ( x + 2 )$

Use a graphing calculator to solve the equation. Round your answer to two decimal places. - $\log _ { 4 } ( x + 2 ) - \log _ { 5 } ( x - 1 ) = 1$

Write as the sum and/or difference of logarithms. Express powers as factors. - $\log _ { 3 } \left( \frac { x ^ { 2 } } { y ^ { 6 } } \right)$

Find functions f and g so that f ° g = H. - $H ( x ) = \frac { 6 } { \sqrt { 9 x + 10 } }$

For the given functions f and g, find the requested composite function. - $f ( x ) = 5 x + 10 , \quad g ( x ) = 5 x - 1 ; \quad$ Find $( f \circ g ) ( x )$

The graph of a one-to-one function f is given. Draw the graph of the inverse function f-1 as a dashed line or curve. - $f(x)=2 x$

For the given functions f and g, find the requested composite function value. - $f ( t ) = \sqrt { t ^ { 4 + 18 t ^ { 2 } + 81 } } , \quad g ( t ) = \frac { t + 3 } { 3 } ; \quad$ Find $( f \circ g ) ( 9 )$ .

Functions and Their Graphs

Linear and Quadratic Functions

Polynomial and Rational Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometric Functions

Polar Coordinates; Vectors

Analytic Geometry

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

Counting and Probability

A Preview of Calculus: the Limit, Derivative, and Integral of a Function

Foundations: a Prelude to Functions

Graphing Utilities

Filters

Exam 4: Exponential and Logarithmic Functions

Choose the one alternative that best completes the statement or answers the question. Find the domain of the composite function f ° g. - f(x)=7x+14;g(x)=x+7f ( x ) = 7 x + 14 ; \quad g ( x ) = x + 7f(x)=7x+14;g(x)=x+7

Write the word or phrase that best completes each statement or answers the question. -What principal invested at 6%, compounded continuously for 3 years, will yield $1500? Round the answer to two decimal places.

Find the amount that results from the investment. - $12,000\$ 12,000$12,000 invested at 5%5 \%5% compounded quarterly after a period of 2 years

Graph the function. - f(x)=e−xf ( x ) = e ^ { - x }f(x)=e−x

Find a formula for the inverse of the function described below. -A size 44 dress in Country C is size 2 in Country D. A function that converts dress sizes in Country C to those in Country D is f(x)=x2−20f ( x ) = \frac { x } { 2 } - 20f(x)=2x​−20 .

Find the amount that results from the investment. - $1,000\$ 1,000$1,000 invested at 4%4 \%4% compounded semiannually after a period of 6 years

Choose the one alternative that best completes the statement or answers the question. The graph of a logarithmic function is shown. Select the function which matches the graph. -

Solve the equation. - log⁡3(3x+7)=log⁡3(3x+2)\log _ { 3 } ( 3 x + 7 ) = \log _ { 3 } ( 3 x + 2 )log3​(3x+7)=log3​(3x+2)

Choose the one alternative that best completes the statement or answers the question. - ln⁡(6x)1+3x9(x−9)7,x>9\ln \frac { ( 6 x ) \sqrt [ 9 ] { 1 + 3 x } } { ( x - 9 ) ^ { 7 } } , \quad x > 9ln(x−9)7(6x)91+3x​​,x>9

The function f is one-to-one. Find its inverse. - f(x)=2x−4f ( x ) = \frac { 2 } { x - 4 }f(x)=x−42​

Solve the problem. Round your answer to three decimals. -What annual rate of interest is required to double an investment in 10 years?

Find the exact value of the logarithmic expression. - ln⁡e8\ln \mathrm { e } ^ { 8 }lne8

Write the word or phrase that best completes each statement or answers the question. Solve the problem. -Determine the domain of the function f(x) f(x)=log⁡5(x+2)f ( x ) = \log _ { 5 } ( x + 2 )f(x)=log5​(x+2)

Use a graphing calculator to solve the equation. Round your answer to two decimal places. - log⁡4(x+2)−log⁡5(x−1)=1\log _ { 4 } ( x + 2 ) - \log _ { 5 } ( x - 1 ) = 1log4​(x+2)−log5​(x−1)=1

Write as the sum and/or difference of logarithms. Express powers as factors. - log⁡3(x2y6)\log _ { 3 } \left( \frac { x ^ { 2 } } { y ^ { 6 } } \right)log3​(y6x2​)

Find functions f and g so that f ° g = H. - H(x)=69x+10H ( x ) = \frac { 6 } { \sqrt { 9 x + 10 } }H(x)=9x+10​6​

For the given functions f and g, find the requested composite function. - f(x)=5x+10,g(x)=5x−1;f ( x ) = 5 x + 10 , \quad g ( x ) = 5 x - 1 ; \quadf(x)=5x+10,g(x)=5x−1; Find (f∘g)(x)( f \circ g ) ( x )(f∘g)(x)

The graph of a one-to-one function f is given. Draw the graph of the inverse function f-1 as a dashed line or curve. - f(x)=2xf(x)=2 xf(x)=2x

For the given functions f and g, find the requested composite function value. - f(t)=t4+18t2+81,g(t)=t+33;f ( t ) = \sqrt { t ^ { 4 + 18 t ^ { 2 } + 81 } } , \quad g ( t ) = \frac { t + 3 } { 3 } ; \quadf(t)=t4+18t2+81​,g(t)=3t+3​; Find (f∘g)(9)( f \circ g ) ( 9 )(f∘g)(9) .

Functions and Their Graphs

Linear and Quadratic Functions

Polynomial and Rational Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometric Functions

Polar Coordinates; Vectors

Analytic Geometry

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

Counting and Probability

A Preview of Calculus: the Limit, Derivative, and Integral of a Function

Foundations: a Prelude to Functions

Graphing Utilities

Filters

Choose the one alternative that best completes the statement or answers the question. Find the domain of the composite function f ° g. - $f ( x ) = 7 x + 14 ; \quad g ( x ) = x + 7$

Find the amount that results from the investment. - $\$ 12,000$ invested at $5 \%$ compounded quarterly after a period of 2 years

Graph the function. - $f ( x ) = e ^ { - x }$ $Graph the function. - f ( x ) = e ^ { - x }$

Find a formula for the inverse of the function described below. -A size 44 dress in Country C is size 2 in Country D. A function that converts dress sizes in Country C to those in Country D is $f ( x ) = \frac { x } { 2 } - 20$ .

Find the amount that results from the investment. - $\$ 1,000$ invested at $4 \%$ compounded semiannually after a period of 6 years

Solve the equation. - $\log _ { 3 } ( 3 x + 7 ) = \log _ { 3 } ( 3 x + 2 )$

Choose the one alternative that best completes the statement or answers the question. - $\ln \frac { ( 6 x ) \sqrt [ 9 ] { 1 + 3 x } } { ( x - 9 ) ^ { 7 } } , \quad x > 9$

The function f is one-to-one. Find its inverse. - $f ( x ) = \frac { 2 } { x - 4 }$

Find the exact value of the logarithmic expression. - $\ln \mathrm { e } ^ { 8 }$

Write the word or phrase that best completes each statement or answers the question. Solve the problem. -Determine the domain of the function f(x) $f ( x ) = \log _ { 5 } ( x + 2 )$

Use a graphing calculator to solve the equation. Round your answer to two decimal places. - $\log _ { 4 } ( x + 2 ) - \log _ { 5 } ( x - 1 ) = 1$

Write as the sum and/or difference of logarithms. Express powers as factors. - $\log _ { 3 } \left( \frac { x ^ { 2 } } { y ^ { 6 } } \right)$

Find functions f and g so that f ° g = H. - $H ( x ) = \frac { 6 } { \sqrt { 9 x + 10 } }$

For the given functions f and g, find the requested composite function. - $f ( x ) = 5 x + 10 , \quad g ( x ) = 5 x - 1 ; \quad$ Find $( f \circ g ) ( x )$

The graph of a one-to-one function f is given. Draw the graph of the inverse function f-1 as a dashed line or curve. - $f(x)=2 x$

For the given functions f and g, find the requested composite function value. - $f ( t ) = \sqrt { t ^ { 4 + 18 t ^ { 2 } + 81 } } , \quad g ( t ) = \frac { t + 3 } { 3 } ; \quad$ Find $( f \circ g ) ( 9 )$ .