$$\text { Find the value of } \mathrm { df } ^ { - 1 } / \mathrm { dx } \text { at } x = f ( a ) \text {. }$$
-$$f ( x ) = 5 x + 6 , a = 2$$
A) 6
B) 5
C) $\frac { 1 } { 6 }$
D) $\frac { 1 } { 5 }$

Question

Quizplus · Accepted Answer

The derivative of $f(x) = 5x + 6$ is $f'(x) = 5$. The inverse function theorem states that $\frac{d}{dx}f^{-1}(x) = \frac{1}{f'(f^{-1}(x))}$. Substituting $x = f(a)$ and $a = 2$, we find $f(2) = 5(2) + 6 = 16$. Thus, $\frac{d}{dx}f^{-1}(x)$ at $x = 16$ is $\frac{1}{5}$, because $f'(x) = 5$ for any $x$.

Find the value of df−1/dx at x=f(a). \text { Find the value of } \mathrm { df } ^ { - 1 } / \mathrm { dx } \text { at } x = f ( a ) \text {. } Find the value of df−1/dx at x=f(a).

$\text { Find the value of } \mathrm { df } ^ { - 1 } / \mathrm { dx } \text { at } x = f ( a ) \text {. }$