Find the following. f(x) = x + 8, g(x) = x − 8

(a) (f + g)(x) =

(b) (f − g)(x) =

(c) (fg)(x) =

(d) (f/g)(x) =

What is the domain of f/g?
(Enter your answer using interval notation.)

(f + g)(x) = 2x

(f - g)(x) = 16

(fg)(x) = - 64

(f/g)(x) = (x + 8)/(x - 8)      Domain:    x < 8 ∪ x > 8

Step-by-step explanation:

(f + g)(x) = f(x) + g(x) = x + 8 + x - 8 = 2x

(f - g)(x) = f(x) - g(x) = x + 8 - (x - 8) = x + 8 - x + 8 = 16

(fg)(x) =  f(x)g(x) = (x + 8)(x - 8) = - 64

(f/g)(x) = f(x)/g(x) = (x + 8)/(x - 8)

              x - 8 ≠ 0

              x ≠ 8

Domain:    x < 8 ∪ x > 8

d

step-by-step explanation:

by observation, we can see that the the graph is simply the graph of y = |x| that has been shifted 4 units downwards and 3 units to the left.

we can recognize in choice d :

y = | x + 3 |   - 4 (rewriting in general form)

y = | x - (- 3) |   - 4

the "-4 " term means   that the graph has been shifted by 4 units in the negative y direction

the "-3 " term means   that the graph has been shifted by 3 units in the negative x direction

this matches our observation of the graph described above.