1. For all real x, let the functions f, g, and h be defined, on the domain of all real numbers, as follows:

f(x) = (x3/3) + (x2/2) + x + 1

g(x) = x3 + x2 + x + 1

h(x) = (x3/3) + (5x2/2) + 6x + 1

Which of these functions have an inverse?

A. f and g only

B. f and h only

C. g and h only

D. f, g, and h

E. The correct answer is not

given by A, B, C, or D.

solution

 

2. Let f(x) = x3 - 8, and let g be the inverse function of f. For what value in the domain of g is g not differentiable?

A. -8

B. -2

C. 0

D. 2

E. 8

solution

 

3. Let f(x) = e^(x3+x2+x) for any real number x, and let g be the inverse function for f. What is g(e3)?

A. 1/(34e39)

B. 1/(6e3)

C. 1/6

D. 6

E. 6e3

solution

 

4. Let f(x) = x3 + x5, and let g be the inverse function of f. What is the value of the derivative g(2)?

A. -1/92

B. 1/92

C. 1/8

D. 8

E. 92

solution