3. Functions

In Exercises 1-10, find f(g(x)) and g (f(x)) and determine whether each pair of functions ƒ and g are inverses of each other. f(x) = 4x and g(x) = x/4

Exercises 123–125 will help you prepare for the material covered in the next section. Solve for y: x = y² -1, y ≥ 0.

Exercises 123–125 will help you prepare for the material covered in the next section. Solve for y : x = 5/y + 4

If f(x) = 3x and g(x) = x + 5, find (ƒ 0 g)¯¹ (x) and (g¯¹ o ƒ˜¹) (x).

In Exercises 59-64, let f(x) = 2x - 5 g(x) = 4x - 1 h(x) = x² + x + 2. Evaluate the indicated function without finding an equation for the function. ƒ¹ (1)

In Exercises 101–102, find an equation for f^(-1)(x). Then graph f and f^(-1) in the same rectangular coordinate system. f(x) = 1 - x^2, x ≥ 0.

Which graphs in Exercises 96–99 represent functions that have inverse functions?

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) = (x - 7)/(x + 2)

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