Answer:
[tex](g\circ h)(x)=-x^2-x-3[/tex]
Step-by-step explanation:
So we have the two functions:
[tex]g(x)=-x-3\text{ and } h(x)=x^2+x[/tex]
And we want to find:
[tex](g\circ h)(x)[/tex]
This is the same thing as:
[tex]=g(h(x))[/tex]
So, substitute h(x) into g(x):
[tex]g(x)=-x-3\\g(h(x))=-(x^2+x)-3[/tex]
Distribute the negative:
[tex]g(h(x))=-x^2-x-3[/tex]
And we're done!
So:
[tex](g\circ h)(x)=-x^2-x-3[/tex]
