Answer:
[tex]g^{-1}[/tex](x) = [tex]\frac{x+10}{5}[/tex]
Step-by-step explanation:
Given
g(x) = 5(x - 2)
let y = g(x) and rearrange making x the subject, that is
y = 5(x - 2) ← distribute
y = 5x - 10 ( add 10 to both sides )
y + 10 = 5x ( divide both sides by 5 )
[tex]\frac{y+10}{5}[/tex] = x
Change y back into terms of x with x = [tex]g^{-1}[/tex] (x) , thus
[tex]g^{-1}[/tex](x) = [tex]\frac{x+10}{5}[/tex]