Exam 10: Compositions, Inverses, and Combinations of Functions

The functions and are defined by the graph below. The dashed graph is and the solid graph is . If , what is ?

Let and . What is ?

LetAnd let What is ?

If , which of the following could be true? Mark all that apply.

For positive numbers x, what is the inverse of ?

Based on the following table, could the function be invertible?

The following figure defines a function f. Which of the following quantities is greater?

The following table gives values for the functions f, g, and h, three functions defined only for the values x = 0, 1, . . . , 5. Based on the table, what is ?

Let And What is ?

Let be the number of men and let be the number of women residing in a certain town in year t. Let be the average income, in dollars, of residents of that town in year t. If and , find a simplified formula for the total amount of money earned by all adult residents of the town in year 3.

Given the graphs of f and g below, evaluate f(g(3)).

Let and . Using the table below gives and .

Let and . Does ?

Let . Does ?

If , which of the following could be true? Mark all that apply.

Let and . Evaluate .

If and , does ?

Let and . Evaluate g to 2 decimal places.

Let and . Does m(n(x)) = ?

Let give the annual profit of a company (in thousands of dollars) t years after its formation. What is ? Round to the nearest whole number and include units.