Suppose that $g$ is the inverse of a function $f$. If $f ( 4 ) = 3$ and $f ^ { \prime } ( 4 ) = 2$, find $g ^ { \prime } ( 3 )$.
A) 3
B) $\frac { 1 } { 2 }$
C)4
D) $\frac { 2 } { 3 }$

Question

Quizplus · Accepted Answer

We can use the formula for the derivative of an inverse function: $g'(f(x)) = \frac{1}{f'(g(f(x)))}$. 
Letting $y=f(4)$, we have $y=3$ and $f'(4)=2$, so $g'(3) = \frac{1}{f'(4)} = \boxed{\frac{1}{2}}$.

Suppose That ggg Is the Inverse of a Function fff If f(4)=3f ( 4 ) = 3f(4)=3

Suppose That $g$ Is the Inverse of a Function $f$ If $f ( 4 ) = 3$