SOLUTION: This is the last question that i have so please someone helppp!!! Find the compositions of the function if: f(x)=x^3+1 , g(x)=x^2-2 , and h(x)=x+3 1.)h(p)= 2.)f(h(x))= 3.)

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Question 46945: This is the last question that i have so please someone helppp!!!
Find the compositions of the function if:
f(x)=x^3+1 , g(x)=x^2-2 , and h(x)=x+3
1.)h(p)=
2.)f(h(x))=
3.)g(g(x))=
4.)h(g(x))=
5.)g(t+h)-g(t) /h= .....(for this one g(t+h)-g(t) iss all divided by h.)
please help!!! thank you!!!
Answer by stanbon(48558) (Show Source):
You can put this solution on YOUR website!
f(x)=x^3+1 , g(x)=x^2-2 , and h(x)=x+3
1.)h(p)=p+3
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2.)f(h(x))=f(x+3)=(x+3)^3+1 = x^3+3x^3+3x+2
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3.)g(g(x))=g(x^2-2)=(x^2-2)^2-2=x^4-4x^2+4-2=x^4-4x^2+2
-----------------------
4.)h(g(x))=h(x^2-2)=(x^2-2)+3=x^2+1
---------------------
5.)[g(t+h)-g(t)] /h= .....(for this one g(t+h)-g(t) iss all divided by h.)
g(t+h)=(t+h)^2-2=t^2+2th+h^2-2
g(t)=t^2-2
Therefore [g(t+h)-g(t)]= 2th+h^2
Now, divide by h to get:
2t+h
Cheers,
Stan H.