Question

Express your answer as a polynomial in standard form.

Answer 1

Answer:

$(f\circ g)(x)=-2x^2-2x+4$

Step-by-step explanation:

So we have the two function:

$f(x)=-x+6\text{ and } g(x)=2x^2+x+2$

And we want to find:

$(f\circ g)(x)$

This is the same as:

$=f(g(x))$

So, substitute g(x) into f(x):

$f(g(x))=-(g(x))+6$

Substitute:

$f(g(x))=-(2x^2+x+2)+6$

Distribute:

$f(g(x))=-2x^2-x-2+6$

Combine like terms:

$f(g(x))=-2x^2-2x+4$

So:

$(f\circ g)(x)=-2x^2-2x+4$

And we're done!