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3-179.

Find the inverse of each of the following functions. Assuming that no domains are restricted, which of the following has an inverse function? How do you know?

$f(x) = −10x + 8$
Step 1(a):
Let $f(x) = y$ .
Step 2(a):
Solve for $x$ .
Step 3(a):
Switch the $x$ and $y$ .

$g(x) = (x + 4)^2$
Hint (b):
Do not forget the $±$ . What will the graph of the inverse look like? Will there be exactly one output for each input?

$f(x) = x^3 + 2$
Hint (c):
To determine if the inverse is a function: Visualize! What does a cube root graph look like?

$h(x) = 3\operatorname{ sin }x$
Hint (d):
If $f(x) =\operatorname{sin}(x)$
Then $f ^{−1}(x) =\operatorname{arcsin}(x) =\operatorname{sin}^{−1}(x)$
Note: $cscx$ is the reciprocal of $\text{sin}x$ , not the inverse!

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