APFIVE Derivative of an Inverse Linear Function
A researcher finds the inverse of the linear function
$$f(x)=3*x+2$$
as
$$f^{-1}(x)=\frac{x-2}{3}$$, and subsequently computes the derivative of the inverse function as a constant $$\frac{1}{3}$$ for all x. Is there any mistake in this process?
A
The error lies in mistakenly differentiating the original function instead of its inverse.
B
The error is in the determination of the inverse function; it should involve an exponentiation rather than a linear expression.
C
The mistake is that the derivative of the inverse should depend on x and not be constant.
D
No mistake; for a linear function, the inverse is also linear and its derivative is constant, correctly computed as $$\frac{1}{3}$$.
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