$$\text { Find the formula for } d f ^ { - 1 } / d x \text {. }$$
-$$f ( x ) = \frac { 1 } { 7 } x + \frac { 9 } { 14 }$$
A) 7
B) $x - \frac { 9 } { 2 }$
C) $\frac { 1 } { 7 }$
D) $7 x - \frac { 9 } { 2 }$

Question

Quizplus · Accepted Answer

The derivative of the inverse function $f^{-1}(x)$ can be found using the formula $\frac{df^{-1}}{dx} = \frac{1}{f'(f^{-1}(x))}$. For $f(x) = \frac{1}{7}x + \frac{9}{14}$, the derivative $f'(x) = \frac{1}{7}$. Thus, the derivative of the inverse function is $\frac{1}{\frac{1}{7}} = 7$.

Find the formula for df−1/dx. \text { Find the formula for } d f ^ { - 1 } / d x \text {. } Find the formula for df−1/dx.

$\text { Find the formula for } d f ^ { - 1 } / d x \text {. }$