Answer:
[tex]g^{-1}[f(9)]=\frac{2}{3}[/tex]
Step-by-step explanation:
To find [tex]g^{-1}(x)[/tex]
instead of g, we write y
[tex]y=3x+4[/tex]
swap x's and y's
[tex]x=3y+4[/tex]
make y subject of the expression
[tex]y=\frac{x-4}{3}\\\implies g^{-1}(x)=\frac{x-4}{3}[/tex]
[tex]g^{-1} \[f(x)\]\quad \textnormal{means put}\quad f \quad \textnormal{in to }\quad g^{-1}[/tex]
[tex]\therefore g^{-1}[f(x)]=\frac{\frac{2x}{3}-4}{3}[/tex]
[tex]=\frac{2x-12}{9}[/tex]
if [tex]x=9[/tex]
[tex]g^{-1}[f(9)]=\frac{2(9)-12}{9}=\frac{18-12}{9}=\frac{6}{9}=\frac{2}{3}[/tex]
