Question

If f(x)= 3x +2 and g(x)=x^2+1, which expression is expression is equivalent to (fog) (x)

Answer 1

Composite Functions

Composite functions occur when we take two functions and input one into the other as x.

Example:

$f(x) = 2x$

$g(x) = 3x^2$

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

$(f\circ g)(x) = 2(3x^2)$

Solving the Question

We're given:

• $f(x)= 3x +2$
• $g(x)=x^2+1$

To find $(f\circ g)(x)$, input g into f as x:

$f(x)= 3x +2$

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

Answer

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