i need help solving this

Question

Find

f + g,

f − g,

fg,

and

f/g

and their domains.

f(x) =

9

x

, g(x) =

11

x + 11

Answer 1

f+g = f(x)+g(x) = (9x) + (11x+11) = 20x + 11

The domain of f+g is all real numbers.

f-g = f(x)-g(x) = (9x) - (11x+11) = -2x -11

The domain of f-g is all real numbers.

fg = f(x)*g(x) = (9x)*(11x+11) = 99x² + 99x

The domain of fg is all real numbers.

f/g = f(x)/g(x) = (9x)/(11x+11)

The domain of f/g is (-∞,-1) ∪ (-1,∞).

Note: if x = -1, then 11x+11 = 11*(-1) + 11 = -11 + 11 = 0. Since we can't divide by zero, we must exclude x = -1 from the domain.