SOLUTION: Composite Functions Given f(x)=x^2-3x+4 ; g(x)=x+2 Find (f o g )(x) (g o f )(2)

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Question 55891: Composite Functions
Given f(x)=x^2-3x+4 ; g(x)=x+2
Find (f o g )(x)
(g o f )(2)
Answer by funmath(2873) About Me  (Show Source):
You can put this solution on YOUR website!
Composite Functions
Given f%28x%29=x%5E2-3x%2B4 ; g%28x%29=x%2B2
Find:
For this one substitute g(x) into f(x):
(f o g )(x)=f(g(x))=f(x+2)=%28x%2B2%29%5E2-3%28x%2B2%29%2B4
=%28x%2B2%29%28x%2B2%29-3%28x%2B2%29%2B4
=%28x%5E2%2B2x%2B2x%2B4%29-3x-6%2B4
=x%5E2%2B4x%2B4-3x-6%2B4
=highlight%28%28fog%29%28x%29=x%5E2%2Bx%2B2%29
:
For this one substitute 2 into f(x) and f(2) into g(x):
(g o f )(2)=g(f(2))=g%28%282%29%5E2-3%282%29%2B4%29=g%284-6%2B4%29=g(2)
g%282%29=%282%29%2B2
highlight%28%28gof%29%282%29=4%29
Happy Calculating!!!