If `f(x)=1-4x`, and `f^(-1)(x)` is the inverse of f(x), then `f(-3)f^(-1)(-3)=`

Options

A. 1
B. 3
C. 4
D. 13

Answer

D

Explanation

First find the inverse of f(x) :
`f(x)=1-4x`
`y=1-4x`
`y+4x=1`
`4x=1-y`
`x=(1-y)/(4)`
`f^(-1)(x)=(1-x)/(4)`
Now find `f(-3)` and `f^(-1)(-3)` :
`f(x)=1-4x`
`f(-3)=1-4(-3)=1-(-12)=13`
`f^(-1)(x)=(1-x)/(4)`
`f^(-1)(-3)=(1-(-3))/(4)=(4)/(4)=1`
And now, to get `f(-3)f^(-1)(-3)`, multiply :
`f(-3)f^(-1)(-3)=13(1)=13`