Compositions of 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.

If f of x = 4x - 7 and g of x = x squared minus 3, find f of g of x and g of f of x and their domains
If f of x = root x minus 1, and g of x = x squared + 2, find f of g of x and g of f of x and their domains
If f of x = root x minus 5, and g of x = 1 minus x squared, find f of g of x and g of f of x and their domains
If f of x = the fraction with numerator 3 and denominator x - 7 and g of x = 1 over x, find f of g of x and g of f of x and their domains
If f of x = the fraction with numerator x and denominator x + 2, find f of f of x and its domain