3. Functions

Find the domain of each function. f(x) = (2x+7)/(x³ - 5x² - 4x+20)

Use each graph to determine an equation of the circle in (a) center-radius form and (b) general form.

Use the graphs of f and g to evaluate each composite function.

(go f) (0)

Find the domain of each function. h(x) = 4/(3/x - 1)

Determine the largest open intervals of the domain over which each function is (a) increasing. See Example 9.

Find the distance between each pair of points. If necessary, express answers in simplified radical form and then round to two decimal places. (4, -1) and (-6, 3)

Determine whether each equation defines y as a function of x. y = ±√(x-2)

Find ƒ+g and determine the domain for each function. f(x) = 2x + 3, g(x) = x − 1

In Exercises 109–111, give the center and radius of each circle. x^2 + y^2 - 4x + 2y - 4 = 0

Exercises 103–105 will help you prepare for the material covered in the next section. Let (x1, y₁) = (7, 2) and (x2, y2) = (1, −1). Find √[(x2 − x1)² + (y2 − y₁)²]. Express the - answer in simplified radical form.

Use the graphs of f and g to solve Exercises 83–90.

Find(g/f)(3)

Find f−g and determine the domain for each function. f(x)= = (5x+1)/(x² - 9), g(x) = (4x -2)/(x² - 9)

Determine whether the three points are the vertices of a right triangle. (-4,3),(2,5),(-1,-6)

Find the value of the function for the given value of x. ƒ(x)=-[[-x]], for x=2.5

To answer each question, refer to the following basic graphs. Which one is the graph of ƒ(x)=√x? What is its domain?