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

1. $p(x)=3(x^3+6)$ 

   Hint (a):

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

   Answer (a):

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

2. $k(x)=3x^3+6$ 

   Hint (b):

   See part (a).

3. $h(x)=\frac{x+1}{x-1}$ 

   Step 1(c):

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

   Step 2(c):

   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.

   Step 3(c):

   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.

   Hint (c):

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

4. $j(x)=\frac{2}{3-x}$ 

   Hint (d):

   See part (a).