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).

Answer 1

First, let's look at the domain and range of f(x) and g(x). f(x) = x has a domain and range of all real numbers while g(x) = √x has a domain and range of all non-negative real numbers.

(f + g)(x) = f(x) + g(x) = x + √x and since we can't take the square root of a negative number while working with real numbers, the domain is all non-negative real numbers

(f - g)(x) = f(x) - g(x) = x - √x and the domain is all non-negative real numbers

(fg)(x) = f(x) * g(x) = x√x = x^(3/2) and the domain is all non-negative real numbers