SOLUTION: if g(x)=x+3 and f(x)=x^2-2, find the value of g(f(x+1)). How do i solve this equation?

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Question 733563: if g(x)=x+3 and f(x)=x^2-2, find the value of g(f(x+1)).
How do i solve this equation?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
"find the value of g(f(x+1))", not certain this is properly asked. You need specific information about some numbers to find a value. Here is what we can do with those two functions about the composition.

From g(x), g(x)=x+3. We want to let x=f(x).
g(__)=(__)+3, put f(x) in the grouping location. g%28f%28x%29%29=f%28x%29%2B3.

We already have a definition for f(x), so we will use this expression:
g%28f%28x%29%29=%28x%5E2-2%29%2B3. BUT THAT IS STILL NOT FINISHED. We are asked for not simply x=f%28x%29, but we are asked for x=f%28x%2B1%29. Then we want:

g%28f%28x%2B1%29%29=f%28x%2B1%29%2B3
g%28f%28x%2B1%29%29=%28%28x%2B1%29%5E2-2%29%2B3
=%28x%5E2%2B2x%2B1+-2%29%2B3
=x%5E2%2B2x-1%2B3
=x%5E2%2B2x%2B4

highlight%28g%28f%28x%2B1%29%29=x%5E2%2B2x%2B4%29