CPM Homework Help : INT3 Problem 7-48

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7-48.

What is the inverse of each of the functions below? Write your answers using function notation.

$p\left(x\right) = 3\left(x^{3} + 6\right)$
Hint (a):
Let $p\left(x\right) = y$ , switch the $x$ and the $y$ in the equation and solve for $y$ .
Answer (a):
$p^{-1}(x)=\sqrt[3]{\frac{x}{3}-6}$

$k\left(x\right) = 3x^{3} + 6$
Hint (b):
See part (a).

$h(x)=\frac{x+1}{x-1}$
Step 1(c):
Let $h\left(x\right) = y$ . Switch $x$ and $y$ . Multiply both sides of the equation by $\left(y − 1\right)$ 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 $\left(x − 1\right)$ to get $y$ by itself.
Hint (c):
Graph the equation on a graphing calculator to see why this equation is its own inverse.

$j(x)=\frac{2}{3-x}$
Hint (d):
See part (a).

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