Given:
[tex]f(x)=4x[/tex]
Required:
We need to find the inverse of the given function.
Explanation:
[tex]\text{ Let f\lparen x\rparen=y and }x=f^{-1}(y)\text{ substitute in the given function.}[/tex][tex]y=4f^{-1}(y).[/tex]
Divide both sides of the equation by 4.
[tex]\frac{y}{4}=\frac{4f^{-1}(y)}{4}[/tex]
[tex]\frac{y}{4}=f^{-1}(y)[/tex]
Replace x =y.
[tex]f^{-1}(x)=\frac{x}{4}[/tex][tex]Let\text{ h\lparen x\rparen =}f^{-1}(x).[/tex][tex]h(x)=\frac{x}{4}[/tex]
Final answer:
[tex]h(x)=\frac{1}{4}x[/tex]
