Question

For the functions f(x) =x^2-9 and g(x) =2x+3 a) Find the function (g/f) (x) b) Find the domain of (g/f) (x)

Answer 1

2x + 3

(g/f)(x) = ------------

x^2 - 9

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all real numbers other than +3 and -3

Explanation:

If: f(x) =x^2-9 and g(x) =2x+3,

then the quotient function (g/f)(x) is as follows:

2x + 3

(g/f)(x) = ------------

x^2 - 9

The denominator here determines the domain: Because we cannot divide by zero, we intentionally set the denominator x^2 - 9 = to zero and solve for x: The solutions are +3 and -3.

The domain consists of "all real numbers other than +3 and -3," or:

(-infinity, -3) ∪ (-3, 3), ∪ (3, infinity)