Answer :
The Composite Function:
Given:
[tex]\begin{gathered} f(x)=-2x^2+4x+6 \\ g(x)=2x-3 \end{gathered}[/tex]It's required to find f(g(2)).
The composite function uses one of the functions and gets it inside of the second function, that is, f(g(x)) is the function f evaluated in g.
First, compute g(2):
[tex]\begin{gathered} g(2)=2\cdot2-3 \\ g(2)=4-1 \\ g(2)=1 \end{gathered}[/tex]Now we take this value and substitute it in f(x):
[tex]\begin{gathered} f(g(2))=f(1) \\ f(g(2))=-2\cdot1^2+4\cdot1+6 \end{gathered}[/tex]Calculating:
[tex]\begin{gathered} f(g(2))=-2+4+6 \\ f\mleft(g\mleft(2\mright)\mright)=8 \end{gathered}[/tex]Answer: 8
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