### Home > CCA2 > Chapter 6 > Lesson 6.2.3 > Problem6-136

6-136.

Find the inverse of each of the functions below. Write your answers in function notation.

1. $p(x)=3(x^3+6)$

Let $p(x)=y$, switch the $x$ and the $y$ in the equation and solve for $y$.

$p^{-1}(x)=\sqrt[{\large 3}]{\frac{x}{3}-6}$

2. $k(x)=3x^3+6$

See part (a).

3. $h(x)=\frac{x+1}{x-1}$

Let $h(x)=y$. Switch $x$ and $y$. Multiply both sides of the equation by $(y−1)$ to remove the fraction.

Distribute and then rewrite the equation so that all the y-terms are on the left side and everything else is on the right side.

Your equation should look like this: $xy−y=x+1$. Factor the left side of the equation and divide both sides by $(x−1)$ to get y by itself.

Graph the equation on a graphing calculator to see why this equation is its own inverse.

4. $j(x)=\frac{2}{3-x}$

See part (a).