Determine the inverse function: Find the inverse function for

If we solve for x as a function of y, we will have a candidate for the inverse. We can then re-express it in terms of x and try out the inverse property. First square both sides and then solve for x:

We can change the independent variable to x and get a more familiar form for our candidate inverse function:

Now we check the definition of the inverse functions:

Test Problem: Find the inverse function, g(x), for y = 3x² + 1.

a)

b)

c)

d)