Question

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

Answer 1

The composite function is

`(f \circ g)(x) = 3x^2 + 5`

Explanation:

Composite functions:

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

`(f \circ g)(x) = f(g(x))`

In this question:

We have that:

`f(x) = 3x + 2`

`g(x) = x^2 + 1`

The composite function is:

`(f \circ g)(x) = f(g(x)) = f(x^2+1) = 3(x^2 + 1) + 2 = 3x^2 + 3 + 2 = 3x^2 + 5`

The composite function is

`(f \circ g)(x) = 3x^2 + 5`