what is the domain?

Question

For f(x)=x^2−9 and g(x)=2x+​3, what is the domain of (f◦​g)(x)?

Answer 1

April, here's how to tackle this:

(f◦​g)(x) = f(g(x))

= f(2x + 3) since g(x) = 2x + 3

= (2x + 3)² - 9 replacing each x in the function f by x + 3

= 4x² + 12x + 9 - 9

= 4x² + 12x

This is valid for all real values of x so the domain of (f◦​g)(x) is all real numbers.