Question

This is the answer I need help on. Could you help me?

Answer 1

The function given is,

`f(x)=(1)/(3)-(1)/(21)x`

We are told to find the inverse function?

SOLUTION

`y=f(x)`

Replace x with y

`\begin{gathered} y=(1)/(3)-(1)/(21)x \\ x=(1)/(3)-(1)/(21)y \end{gathered}`

Solve for y

Collect like terms

`(1)/(21)y=(1)/(3)-x`

Multiply both sides by 21

`\begin{gathered} 21*(1)/(21)y=21*(1)/(3)-21* x \\ y=7-2x \\ \therefore y=7-21x \end{gathered}`

Hence,

`f^(-1)(x)=7-21x`

The correct option is Option D.