In Exercises 55–59, use the graph of to graph each function g.

g(x) = f(x + 2) + 3

In Exercises 60–63, begin by graphing the standard quadratic function, f(x) = x². Then use transformations of this graph to graph the given function. r(x) = -(x + 1)²

In Exercises 64–66, begin by graphing the square root function, f(x) = √x. Then use transformations of this graph to graph the given function. g(x) = √(x + 3)

In Exercises 64–66, begin by graphing the square root function, f(x) = √x. Then use transformations of this graph to graph the given function. r(x) = 2√(x + 2)

In Exercises 67–69, begin by graphing the absolute value function, f(x) = |x|. Then use transformations of this graph to graph the given function. r(x) = (1/2) |x + 2|

Find the domain of each function. g(x) = 4/(x - 7)

Find the domain of each function. $f\left(x\right)=x/(x^2+4x-21)$

Find f + g, f - g, fg, and f/g. f(x) = x² + x + 1, g(x) = x² -1

Find a. (f ○ g)(x); b. the domain of (f ○ g). f(x) = (x + 1)/(x - 2), g(x) = 1/x

Express the given function h as a composition of two functions f and g so that h(x) = (f ○ g)(x). h(x) = (x² + 2x - 1)⁴

The functions in Exercises 93–95 are all one-to-one. For each function, (a) find an equation for f^-1(x), the inverse function. (b) Verify that your equation is correct by showing that f(f^-1(x)) = x and f^-1(f(x)) = x. f(x) = 4x - 3