3. Functions

Determine whether each relation defines a function, and give the domain and range.

An equation that defines y as a function of x is given. Find ƒ(3). x-4y=8

Find the domain of each function. f(x) = √(24 - 2x)

Graph each function. Give the domain and range. g(x)=[[2x-1]]

Let ƒ(x)=-3x+4 and g(x)=-x²+4x+1. Find each of the following. Simplify if necessary. g(-x)

For the points P and Q, find (a) the distance d(P, Q) and (b) the coordinates of the mid-point M of line segment PQ. P(6,-2), Q(4,6)

Find ƒ+g, ƒ- g, ƒg and ƒ/g. Determine the domain for each function. f(x) = 3 − x², g(x) = x² + 2x − 15

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

Find the domain of ƒ + g.

Give a rule for each piecewise-defined function. Also give the domain and range.

Find a. (fog) (x) b. (go f) (x). f(x) = √x, g(x) = x − 1

Find

a. (fog) (x)

b. (go f) (x)

c. (fog) (2)

d. (go f) (2).

f(x) = x+4, g(x) = 2x + 1

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

Find a. (fog) (x) b. the domain of f o g.

f(x) = x² + 4, g(x) = √(1 − x)

Find the coordinates of the other endpoint of each line segment, given its midpoint and one endpoint. See Example 5(b).

midpoint $(12,6)$, endpoint $(19,16)$

In Exercises 107–108, write the standard form of the equation of the circle with the given center and radius. Center (-2. 4), r = 6