Question

Let f(x) = 4x – 5 and g(x) = 3x + 7. Find f(x) + g(x) and state its domain.

Answer 1

f(x) = 4x - 5

g(x) = 3x + 7

Both of them have no existence conditions, so both has real as they domain

f(x) + g(x) = (4x - 5) + (3x + 7) = 4x + 3x + 7 - 5 = 7x + 2

Since both has real as they domain, f(x) + g(x) will too.

Answer 2

ƒ(x) + g(x) = 7x - 2

(-∞, ∞) or -∞ < x < ∞

Explanation:

ƒ(x) = 4x - 5

g(x) = 3x + 7

ƒ(x) + g(x) = 4x - 5 + 3x + 7 = 7x - 2

The domain is the set of all possible x-values that will make a function work.

x can take any value from -∞ to ∞.

The domain is (-∞, ∞) or -∞ < x < ∞.

The diagram shows the graphs of ƒ(x) (red), g(x) (blue), and the solid green line is the graph of ƒ(x) + g(x). The line extends indefinitely in both directions,