CPM Homework Help : PC3 Problem 6-106

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6-106.

What is the inverse of each function below? Use correct notation.

$h(x)=2x^{3/2}$
Step (a):
$x=2y^{3/2}$

$j(x)=4\log_5(x-1)$
Step 1(b):
$x=4\log_5(y-1)$
Step 2(b):
$\frac{x}{4}=\log_5(y-1)$
Step 3(b):
$5^{x/4}=y-1$

$f(x)=4(2x-3)^{1/3}$

Step 1(c):
$x=4(2y-3)^{1/3}$
Step 2(c):
$\frac{x}{4}=(2y-3)^{1/3}$
Step 3(c):
$\left(\frac{x}{4}\right)^3=2y-3$

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