Question

(F x G)(x) F(G(x)) G[F(x)] F[G(x)] G(F(x))

Answer 1

The results of the composite functions are:

• $(f \times g)(x) = 6x^2-9x$

• $f(g(x)) = 6x - 3$

• $g(f(x)) = 6x - 9$

What are composite functions?

Composite functions are functions that are obtained by combining two or more functions together

Assume that:

• $f(x) = 2x - 3$

• $g(x) = 3x$

Then the computation of the composite functions are as follows:

Function (f * g)(x)

$(f \times g)(x) = f(x) \times g(x)$

$(f \times g)(x) = (2x-3) \times (3x)$

$(f \times g)(x) = 6x^2-9x$

Function f(g(x))

We have: $f(x) = 2x - 3$

This gives

$f(g(x)) = 2g(x) - 3$

So, we have:

$f(g(x)) = 2(3x) - 3$

$f(g(x)) = 6x - 3$

Function g(f(x))

We have: $g(x) = 3x$

This gives

$g(f(x)) = 3f(x)$

So, we have:

$g(f(x)) = 3(2x - 3)$

$g(f(x)) = 6x - 9$

Read more about composite functions at:

brainly.com/question/10687170