Derivative of an Inverse Function

Question

Let $$f(x)=3*x+5$$. Its inverse $$f^{-1}(x)$$ satisfies certain derivative properties. All of the following statements are true except:

Accepted Answer

The derivative of the inverse function is $$(f^{-1})'(x)=3$$.

Answer

For $$f(x)=3*x+5$$, the derivative $$f'(x)$$ is 3.

Answer

Differentiating the identity $$f(f^{-1}(x))=x$$ using the chain rule leads to $$f'(f^{-1}(x))*(f^{-1})'(x)=1$$.

Answer

Using the formula $$(f^{-1})'(x)=1/f'(f^{-1}(x))$$, the derivative of the inverse function is $$\frac{1}{3}$$.

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