someone please help medal award! Given f(x)=x^2-3 and g(x)=x+2, find the following (write in general form). a) f(g(x)) b) g(f(x)) c. f(f(x)) d. evaluate f(g(-5))

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someone please help medal award! Given f(x)=x^2-3 and g(x)=x+2, find the following (write in general form). a) f(g(x)) b) g(f(x)) c. f(f(x)) d. evaluate f(g(-5))

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Okay so first things first. Put g(x) inside the f(x) equation.
For a)
would I have to multiply x^2-3 by x+2? for a?

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Other answers:

\[(x+2)^2 -3\]
you replace the x from f(x) with the equation of g(x)
oh i see I got x^2+4x+1
Correct
You do basically the opposite for B) You use the g(x) equation and replace the x with the f(x) equation
but how would you set it up since theres a -3 and a 2?
You replace X with (X^2 -3) +2
+2 is from g(x) = x "+2"
I got X^2-1
and for f I believe it's set up as (x^2-3)-3
for f(f(x))?
the X^2-1 I got for problem b I simplified it, and I set up (x^2-3)+2 for problem c
and for f I set it up as g(-5)=(-5+2)^2-3
Yes for B that is correct, But for c) you use f(f(x)). You do not use g(x) in the question.
so for c it would be (x^2-3)(x^2-3)?
\[f(f(x)) = (x^2 - 3)^2-3\]
and c factors out to x^4-6x^2+6 :)
Correct! :)
thanks so much :-) for d I got 6 I wasn't sure if I set it up correctly I set it up as (-5+2)^2-3
That's what I got too, and np! :)
thanks so much for all your help :D

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