3. Functions

Find a. (fog) (x) b. (go f) (x) c. (fog) (2) d. (go f) (2).

f(x) = 1/x, g(x)= 1/x

Find f−g and determine the domain for each function. f(x) = x -5, g(x) = 3x²

Solve and check: (x-1)/5 - (x+3)/2 = 1- x/4

Find a. (fog) (x) b. (go f) (x) f(x)=4x-3, g(x) = 5x² - 2

Find ƒ+g and determine the domain for each function. f(x) = √(x +4), g(x) = √(x − 1)

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

midpoint $(6a,6b)$, endpoint $(3a,5b)$

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(-5,-6), Q(7,-1)

Determine the intervals of the domain over which each function is continuous.

In Exercises 65–70, use the graph of f to find each indicated function value. f(-3)

Find the domain of $f\(\left\)(x\(\right\))=\(\frac{1}{x^2-5x+6}\)$ . Express your answer using interval notation.

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

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

In Exercises 31–50, find f−g and determine the domain for each function. f(x) = √(x +4), g(x) = √(x − 1)

Find fg and determine the domain for each function. f(x)= = 8x/(x - 2), g(x) = 6/(x+3)

Determine whether the three points are the vertices of a right triangle. See Example 3.

$(-2,-5),(1,7),(3,15)$