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`