The function given is,
[tex]f(x)=\frac{1}{3}-\frac{1}{21}x[/tex]
We are told to find the inverse function?
SOLUTION
[tex]y=f(x)[/tex]
Replace x with y
[tex]\begin{gathered} y=\frac{1}{3}-\frac{1}{21}x \\ x=\frac{1}{3}-\frac{1}{21}y \end{gathered}[/tex]
Solve for y
Collect like terms
[tex]\frac{1}{21}y=\frac{1}{3}-x[/tex]
Multiply both sides by 21
[tex]\begin{gathered} 21\times\frac{1}{21}y=21\times\frac{1}{3}-21\times x \\ y=7-2x \\ \therefore y=7-21x \end{gathered}[/tex]
Hence,
[tex]f^{-1}(x)=7-21x[/tex]
The correct option is Option D.
