Question

Use the pair of functions to find f(g(x)) and g(f(x)) . Simplify your answers.

Answer 1

ANSWERS

• f(g(x)) = sqrt(x² + 9) + 8

,

• g(f(x)) = x + 16sqrt(x) + 73

Step-by-step explanation

To find the composition f(g(x)), we have to replace x with g(x) in the function f(x),

`f(g)=√(g(x))+8=√(x^2+9)+8`

This function is in its simplest form.

To find the composition g(f(x)), we have to replace x with f(x) in the function g(x),

`g(f)=f^2+9=(√(x)+8)^2+9`

We can simplify this by expanding the binomial squared,

`g(f(x))=(√(x))^2+16√(x)+64+9=x+16√(x)+73`

Hence, the two compositions are:

• f(g(x)) = sqrt(x² + 9) + 8

,

• g(f(x)) = x + 16sqrt(x) + 73