SOLUTION: If f(x)=2x+3 and g(x)=x^2-2x+3, determine (GoF).

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Question 164402: If f(x)=2x+3 and g(x)=x^2-2x+3, determine (GoF).
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Remember GoF is shorthand notation for g(f(x))


g%28x%29=x%5E2-2x%2B3 Start with the given function


g%28f%28x%29%29=%282x%2B3%29%5E2-2%282x%2B3%29%2B3 Plug in f%28x%29=2x%2B3


g%28f%28x%29%29=%284x%5E2%2B12x%2B9%29-2%282x%2B3%29%2B3 FOIL


g%28f%28x%29%29=4x%5E2%2B12x%2B9-4x-6%2B3 Distribute


g%28f%28x%29%29=4x%5E2%2B8x%2B6 Combine like terms.


So GoF is g%28f%28x%29%29=4x%5E2%2B8x%2B6