Exam 12: Exponential Functions and Logarithmic Functions

Graph the equation of the relation using a solid line, and then graph the inverse of the relation using a dashed line. - $y = 7 x ^ { 2 } + 2 x$

Find the requested composition of functions. -Given $f ( x ) = \frac { 3 } { x }$ and $g ( x ) = 2 x ^ { 2 }$ , find $g f ( x )$ .

Find f(x)and g(x)such that h(x)= (f ° g)(x). - $h ( x ) = \sqrt { 58 x ^ { 2 } + 92 }$

Find f(x)and g(x)such that h(x)= (f ° g)(x). - $h ( x ) = \frac { x ^ { 5 } - 4 } { x ^ { 5 } + 2 }$

Graph. - $f(x)=3 x-1$

Solve the problem. -An accountant tabulated a firm's profits for four recent years in the following table: Year Profits 1996 \ 250,000 1997 \ 300,000 1998 \ 400,000 1999 \ 600,000 The accountant then fit both a linear graph and an exponential curve (seen below) to the data, in order to estimat profits. Use the linear graph to estimate the profits in the year $2001 .$

Graph the relation using solid circles and the inverse using open circles. - $\{ ( - 1,16 ) , ( - 7 , - 2 ) , ( 5 , - 11 ) \}$

Solve the problem. -The number of bacteria growing in an incubation culture increases with time according to $\mathrm { B } ( \mathrm { x } ) = 9800 ( 2 ) ^ { \mathrm { x } }$ , where $x$ is time in days. Find the number of bacteria when $x = 0$ and $x = 3$ .

Determine whether the function is one-to-one. - $f ( x ) = \left( \frac { 1 } { 3 } \right) ^ { x }$

Determine whether the given function is one-to-one. If so, find a formula for the inverse. - $f ( x ) = \frac { 4 x - 7 } { 2 x + 6 }$

Find the requested composition of functions. -Given $f ( x ) = \frac { 6 } { x ^ { 2 } }$ and $g ( x ) = x - 3$ , find $g f ( x )$

Find f(x)and g(x)such that h(x)= (f ° g)(x). - $h ( x ) = 6 ( 8 x + 7 ) ^ { 2 } - 9$

Find the requested composition of functions. -Given $f ( x ) = \frac { x - 10 } { 7 }$ and $g ( x ) = 7 x + 10$ , find $g f ( x )$ .

Find f(x)and g(x)such that h(x)= (f ° g)(x). - $h ( x ) = \frac { 1 } { x ^ { 2 } - 5 }$

Find the requested composition of functions. -Given $f ( x ) = 7 x + 8$ and $g ( x ) = 5 x - 1$ , find $f g ( x )$ .

Graph the relation using solid circles and the inverse using open circles. - $\{ ( - 6,7 ) , ( - 7,6 ) , ( - 9 , - 4 ) , ( 9,4 ) \}$

Determine whether the function is one-to-one. - $f ( x ) = 4 x ^ { 2 } + x$

Graph. - $f(x)=\left(\frac{1}{3}\right)^{x}+2$

Find the requested composition of functions. -Given $f ( x ) = x ^ { 2 } + 8$ and $g ( x ) = x ^ { 2 } - 8$ , find $f g ( x )$ .

Find an equation of the inverse of the relation. - $y = 3 x ^ { 2 } + 5 x$