Inverse Functions

Each of the problems below is a link. If you click on the problem, it will take you to a YouTube video of a full, step-by-step solution for the problem. You may try these problems as practice and use the videos to check your answer, or you can just watch the videos to see more worked-out example problems.

Show that f of x = x + 1 and g of x = x minus 1 are inverse functions
Show that f of x = 7x + 2 and g of x = the fraction with numerator x minus 2 and denominator 7 are inverse functions
Show that f of x = the fraction with numerator 3 minus x and denominator 4 and g of x = 3 minus 4x are inverse functions
Show that f of x = x cubed + 1 and g of x = left paren x minus 1 right paren to the 1 third power are inverse functions
We know that f of x = x squared is not a one-to-one function. How can we restrict its domain so that its inverse function is g of x = root x
We know that f of x = x squared is not a one-to-one function. How can we restrict its domain so that its inverse function is g of x = negative root x