To answer this question we will set the equation y=f(x), then we will solve the equation for x, and finally, we will exchange x and y.
Setting y=f(x) we get:
[tex]y=\frac{3}{4}x+12.[/tex]
Subtracting 12 from the above equation we get:
[tex]\begin{gathered} y-12=\frac{3}{4}x+12-12, \\ y-12=\frac{3}{4}x\text{.} \end{gathered}[/tex]
Multiplying the above equation by 4/3 we get:
[tex]\begin{gathered} (y-12)\times\frac{4}{3}=\frac{3}{4}x\times\frac{4}{3}, \\ x=\frac{4}{3}y-16. \end{gathered}[/tex]
Exchanging x and y in the above equation we get:
[tex]y=\frac{4}{3}x-16.[/tex]
Therefore the inverse function of h(x) is:
[tex]h^{-1}(x)=\frac{4}{3}x-16.[/tex]
Answer:
[tex]h^{-1}(x)=\frac{4}{3}x-16.[/tex]
