Answer:
[tex](f\circ g)(x)=-2x^2-2x+4[/tex]
Step-by-step explanation:
So we have the two function:
[tex]f(x)=-x+6\text{ and } g(x)=2x^2+x+2[/tex]
And we want to find:
[tex](f\circ g)(x)[/tex]
This is the same as:
[tex]=f(g(x))[/tex]
So, substitute g(x) into f(x):
[tex]f(g(x))=-(g(x))+6[/tex]
Substitute:
[tex]f(g(x))=-(2x^2+x+2)+6[/tex]
Distribute:
[tex]f(g(x))=-2x^2-x-2+6[/tex]
Combine like terms:
[tex]f(g(x))=-2x^2-2x+4[/tex]
So:
[tex](f\circ g)(x)=-2x^2-2x+4[/tex]
And we're done!
