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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?

1. $f(x) = −10x + 8$

Let $f(x) = y$.

Solve for $x$.

Switch the $x$ and $y$.

1. $g(x) = (x + 4)^2$

Do not forget the $±$. What will the graph of the inverse look like? Will there be exactly one output for each input?

1. $f(x) = x^3 + 2$

To determine if the inverse is a function: Visualize! What does a cube root graph look like?

1. $h(x) = 3\operatorname{ sin }x$

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!