CPM Homework Help : CALC Problem 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 ✎
1. f(x) = −10x + 8
2. g(x) = (x + 4)²
3. f(x) = x³ + 2
4. h(x) = 3 sin x

Step 1(a):

Let f(x) = y.

Step 2(a):

Solve for x.

Step 3(a):

Switch the x and y.

Hint (b):

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

Hint (c):

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

Hint (d):

If f(x) = sin(x)
Then f ⁻¹(x) = arcsin(x) = sin⁻¹(x)
Note: cscx is the reciprocal of sinx, not the inverse!