h(x)=1/4x
Step-by-step explanation:
To find the inverse of a function, switch the "x" and the "y". The f(x) can be considered as "y".
![f(x)=4x](/tpl/images/0747/9316/f7d9e.png)
![y=4x](/tpl/images/0747/9316/bd48f.png)
![x=4y](/tpl/images/0747/9316/8df2d.png)
We want to isolate y. 4 and y are being multiplied. The inverse of multiplication is division. Divide both sides of the equation by 4.
![\frac{x}{4} =\frac{4y}{4}](/tpl/images/0747/9316/29da9.png)
![\frac{x}{4} =y](/tpl/images/0747/9316/e57e0.png)
x/4 can be rewritten as 1/4x.
![y=\frac{1}{4} x](/tpl/images/0747/9316/788a1.png)
![h(x)=\frac{1}{4} x](/tpl/images/0747/9316/1881f.png)
The inverse of the function f(x)=4x is h(x)=1/4x