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) = (x^{3}/3) + (x^{2}/2) + x + 1 |
g(x) = x^{3 }+ x^{2 }+ x + 1 |
h(x) = (x^{3}/3) + (5x^{2}/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. |
2. Let f(x) = x^{3} - 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 |
3. Let f(x) = e^(x^{3}+x^{2}+x) for any real number x, and let g be the inverse function for f. What is g(e^{3})?
A. 1/(34e^{39}) |
B. 1/(6e^{3}) |
C. 1/6 |
D. 6 |
E. 6e^{3} |
4. Let f(x) = x^{3} + x^{5}, 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 |