Question

If the function f(x) = 1 + x + $\frac{x^{2}}{2}$+ $\frac{x^{3}}{3}$ – $3e^{\frac{1 - x}{3}}$ and

g(x) = f^–1(x), then the value of g¢$\left( - \frac{1}{6} \right)$ equals

• A. –$\frac{1}{6}$
• B. –$\frac{6}{5}$
• C. $\frac{1}{4}$
• D. 4

Answer 1

Answer: (C)

$\frac{1}{4}$

Answer 2

g¢(–1/6) = 1/f¢(1) = ¼

f(1) = 2 +$\frac{1}{6}$– 3 = –$\frac{1}{6}$

̃ f ¢(1) = 1 + 1 + 1 –3$\left( - \frac{1}{3} \right)$