Given f(x) and g(x) below, find and simplify (f o g)(x) and find its domain.

Question

 f(x) = x^2 - 7

g(x) = sqrt(20 - 5 x)

 

(f o g)(x) =?

 

The domain of (f o g)(x) is ?

Answer 1

Hi Alexandria,

 

This is a composite function question.

(fog)(x) = f(g(x))

We are given the equations of f(x) and g(x)

So we can simply plug them in

f(g(x)) = f(sqrt(20 - 5 x))

f(sqrt(20 - 5 x))=(sqrt(20-5x))^2-7

=20-5x-7

=-5x+13

The domain (i.e., the values x can take) for this function is all real numbers.