Respuesta :

MrRoyal

The results of the composite functions are:

  • [tex](f \times g)(x) = 6x^2-9x[/tex]
  • [tex]f(g(x)) = 6x - 3[/tex]
  • [tex]g(f(x)) = 6x - 9[/tex]

What are composite functions?

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

Assume that:

  • [tex]f(x) = 2x - 3[/tex]
  • [tex]g(x) = 3x[/tex]

Then the computation of the composite functions are as follows:

Function (f * g)(x)

[tex](f \times g)(x) = f(x) \times g(x)[/tex]

[tex](f \times g)(x) = (2x-3) \times (3x)[/tex]

[tex](f \times g)(x) = 6x^2-9x[/tex]

Function f(g(x))

We have: [tex]f(x) = 2x - 3[/tex]

This gives

[tex]f(g(x)) = 2g(x) - 3[/tex]

So, we have:

[tex]f(g(x)) = 2(3x) - 3[/tex]

[tex]f(g(x)) = 6x - 3[/tex]

Function g(f(x))

We have: [tex]g(x) = 3x[/tex]

This gives

[tex]g(f(x)) = 3f(x)[/tex]

So, we have:

[tex]g(f(x)) = 3(2x - 3)[/tex]

[tex]g(f(x)) = 6x - 9[/tex]

Read more about composite functions at:

https://brainly.com/question/10687170

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