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

Question

f(x) = 4 − x,    g(x) = x² − 3x



Find (f + g)(x).

 

Find the domain of (f + g)(x).

 (Enter your answer using interval notation.)

 

Find (f − g)(x).

 

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 (f/g)(x)

Find the domain of (f/g)(x). (Enter your answer using interval notation.)

Answer 1

You add, subtract, multiply, and divide polynomials just by adding, subtracting, multiplying, and dividing the polynomials.

For example, if f(x) = x² + 5 and g(x) = x - 7, then

(f-g)(x) = (x² + 5) - (x - 7) = x² + 5 - x + 7 = x² - x + 12