Torrez503 Torrez503
  • 13-04-2021
  • Mathematics
contestada

If F(x) = 3x + 2 and g(x) = x2 + 1, which expression is equivalent to (f°g)(x)?

Respuesta :

joaobezerra joaobezerra
  • 18-04-2021

Answer:

The composite function is

[tex](f \circ g)(x) = 3x^2 + 5[/tex]

Step-by-step explanation:

Composite functions:

Suppose that we have two functions, f and g. Their composite is given by:

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

In this question:

We have that:

[tex]f(x) = 3x + 2[/tex]

[tex]g(x) = x^2 + 1[/tex]

The composite function is:

[tex](f \circ g)(x) = f(g(x)) = f(x^2+1) = 3(x^2 + 1) + 2 = 3x^2 + 3 + 2 = 3x^2 + 5[/tex]

The composite function is

[tex](f \circ g)(x) = 3x^2 + 5[/tex]

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