We will illustrate on how to find the inverse function.
First, recall that the inverse function is a function that given the output of a function, it will give you back the input out of which that output came from.
when athe function has a formula, we can follow some steps to find the inverse function. Suppose we are given the function
[tex]f(x)=3x+5[/tex]
Now, we first change f(x) with the letter y. So we get
[tex]y=3x+5[/tex]
now, we interchange variables x and y. So we get
[tex]x=3y+5[/tex]
Finally we solve this equation for y. We will first subtract 5 on both sides and then divide both sides by 3. So we get
[tex]y=\frac{x\text{ -5}}{3}[/tex]
and now we replace the y with the symbol of the inverse function. So we have that
[tex]f^{\text{ -1}}(x)=\frac{x\text{ -5}}{3}[/tex]
