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) = −10x + 8
g(x) = (x + 4)2
f(x) = x3 + 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: cscx is the reciprocal of sinx, not the inverse!