Answer:
[tex]g^{-1}[/tex](x) = [tex]\frac{5x+45}{3}[/tex]
Step-by-step explanation:
let y = g(x) and rearrange making x the subject
y = [tex]\frac{3}{5}[/tex] x - 9 ( add 9 to both sides )
y + 9 = [tex]\frac{3}{5}[/tex] x
Multiply both sides by 5 to clear the fraction
5y + 45 = 3x ( divide both sides by 3 )
[tex]\frac{5y+45}{3}[/tex] = x
Change y back into terms of x, thus
[tex]g^{-1}[/tex](x) = [tex]\frac{5x+45}{3}[/tex]
