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: The answer is B
First, by the wording of the problem, we can assume that the inverse exists in a neighborhood of x = e3, i.e., when x = 1.
Second, by the definition of the inverse function g(f(x)) = x. Consequently
Third, by inspection, when x = 1,
|
f(1) = e3 |
|
f'(x) = (3x2 +2x +1) e^(x3+x2+x) |
|
f'(1)=6 e3 |
Thus
