Question

suppose that the functions f and g are defined as follows. find g/f. then, give its domain using an interval or Union of intervals. simplify your answers. Edit: please double check the answers.

Answer 1

Step 1: Write out the given functions

`f(x)=(9)/(x),g(x)=(4)/(x+2)`

Step 2: Find 1/f and g/f

`(1)/(f)(x)=(x)/(9)`

Therefore,

`(g)/(f)(x)=(4)/(x+2)*(x)/(9)=(4x)/(9(x+2))`

The domain of f is (-∞, ∞) \ {0}.

The domain of g is (-∞, ∞)

If x + 2 = 0, then x = -2.

Therefore g/f is undefined at x = -2.

Hence, the domain of g/f is (-∞, ∞) \ {-2,0}.

Therefore, the domain of g/f is (-∞, -2) ∪ (-2, 0) ∪ (0, ∞)