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)=(x)/(4)\text{ , for all x} \end{gathered}`

Option C is the final answer.

b)

`\begin{gathered} f(f^(-1)(x))=f((x)/(4)) \\ =4((x)/(4)) \\ =x \end{gathered}`
`\begin{gathered} f^(-1)(f(x))=f^(-1)(4x) \\ =(4x)/(4) \\ =x \end{gathered}`
`f(f^(-1)(x))=f^(-1)(f(x))=x`