Question

If f(x)=5x+7 and g(x)=√x+6, which statement is true?

A.) 9 is not in the domain of f ° g
B.) 9 is in the domain of f ° g

Answer 1

Statement b is true; statement a is false

Explanation:

Best to write out (f o g)(x) and then determine its domain:

"(f o g)(x)" indicates that g(x) is used as the input to f(x):

(f o g)(x) = 5(√x+6) + 7, or 5√x + 30 + 7, or 5√x + 37.

The domain of this composite function is [0, infinity).

Thus, statement b is true: "9 is part of the domain of (f o g)(x) = 5(√x+6) + 7"