Question

The function f(x)= 4x is one to one Find A and B

Answer 1

Given:

$f(x)=4x$

a)

$\begin{gathered} x=4f^{-1}(x) \\ f^{-1}(x)=\frac{x}{4}\text{ , for all x} \end{gathered}$

Option C is the final answer.

b)

$\begin{gathered} f(f^{-1}(x))=f(\frac{x}{4}) \\ =4(\frac{x}{4}) \\ =x \end{gathered}$$\begin{gathered} f^{-1}(f(x))=f^{-1}(4x) \\ =\frac{4x}{4} \\ =x \end{gathered}$$f(f^{-1}(x))=f^{-1}(f(x))=x$