Find f + g, f − g, fg, and f/g and their domains.

Question

f(x) = x, g(x) = square root x

Find

(f + g)(x

Find the domain of

(f + g)(x). (Enter your answer using interval notation.)

Find the domain of

(f − g)(x).(Enter your answer using interval notation.)

Find (fg)(x).

Find the domain of

(fg)(x). (Enter your answer using interval notation.)

Find fg(x).

Find the domain of fg(x). (Enter your answer using interval notation.)

Answer 1

first let's look at domain of f and g:

domain of f(x): (-∞,∞)

domain of g(x): [0, ∞)

1. (f + g)(x) = x + √x , has the same limitations as g(x), i.e., same domain as g(x)
2. (f - g)(x) = x - √x , has the same limitations as g(x), i.e., same domain as g(x)
3. fg(x) = x^1.5, like g(x) x can not be negative so same domain as g(x) - I assume that you mean multiply the two functions together
4. f(g(x)) = √x, same as g(x) - I assume this means composite function