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find the inverse of the function f(x)=-2/3x-18 show work

A g(x)=3/2x+27


B g(x)=-3/2x+27


C g(x)=-3/2x-27

D g(x)=3/2x-27

Respuesta :

C

let y = f(x)

Then rearrange making x the subject

y = - [tex]\frac{2}{3}[/tex] x - 18 ( add 18 to both sides )

y + 18 = - [tex]\frac{2}{3}[/tex] x

multiply both sides by -  [tex]\frac{3}{2}[/tex]

- [tex]\frac{3}{2}[/tex] (y + 18) = x

x = - [tex]\frac{3}{2}[/tex] y - 27

change y to x for inverse function

[tex]f^{-1}[/tex](x) = - [tex]\frac{3}{2}[/tex] x - 27 → C


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