Question

Given that f(x) = x2 + 5x + 6 and g(x) = x + 2, find (fºg)(x) and

express the result in standard form.
US

Answer 1

`(f\circ g)(x)=x^2+9x+20`

Explanation:

We have the two functions:

`f(x)=x^2+5x+6\text{ and } g(x)=x+2`

And we want to find:

`(f\circ g)(x)`

This is equivalent to:

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

Therefore, we will have:

`f(x+2)`

By substitution:

`f(x+2)=(x+2)^2+5(x+2)+6`

Simplify. Square and distribute:

`f(x+2)=(x^2+4x+4)+(5x+10)+6`

Rearrange:

`f(x+2)=(x^2)+(4x+5x)+(4+10+6)`

Combine like terms:

`f(x+2)=(f\circ g)(x)=x^2+9x+20`