Answer:
[tex]f(g(-2))=11[/tex]
Step-by-step explanation:
We are given the two functions:
[tex]f(x)=x^2-2x+3\text{ and } g(x)=x^2-2x-4[/tex]
And we want to find:
[tex]f(g(-2))[/tex]
We will find g(-2) first. So:
[tex]g(-2)=(-2)^2-2(-2)-4=4+4-4=4[/tex]
Thus:
[tex]f(g(-2))=f(4)[/tex]
Evaluate:
[tex]f(4)=(4)^2-2(4)+3=16-8+3=11[/tex]
Therefore:
[tex]f(g(-2))=11[/tex]
