Question

4. Let f(x) = x + 2 and g(x) = 2x^2. Perform the function operation belowand then find the domain of the result. (g/f)(x)

Answer 1

(g/f)(x) = g(x)/f(x) = 2x²/(x+2)

The domain is all real values of x except x = -2

Explanation:

We are given these following functions:

f(x) = x + 2

g(x) = 2x²

(g/f)(x)

This is g divided by f. So

(g/f)(x) = g(x)/f(x) = 2x²/(x+2)

Domain:

When we have a fraction, we have a constraint, that states that the denominator cannot be 0.

In this question, for (g/f)(x), the denomiator is x + 2.

For the domain, we need that:

x + 2 != 0

x != -2

So

The domain is all real values of x except x = -2