### Home > CALC > Chapter Ch3 > Lesson 3.4.3 > Problem 3-179

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? Homework Help ✎*f*(*x*) = −10*x*+ 8*g*(*x*) = (*x*+ 4)^{2}*f*(*x*) =*x*^{3}+ 2*h*(*x*) = 3 sin*x*

Let *f*(*x*) = *y*.

Solve for *x*.

Switch the *x* and *y*.

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

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

If *f*(*x*) = sin(*x*)

Then *f* ^{−1}(*x*) = arcsin(*x*) = sin^{−1}(*x*)

Note: csc*x* is the reciprocal of sin*x*, not the inverse!