Question

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

Answer 1

Answer:

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

Step-by-step 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:

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