SOLUTION: if f(x)=2x+1 and g(x)= x-1 over 2 then f(g(x))= ?

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Question 375581: if f(x)=2x+1 and g(x)= x-1 over 2 then f(g(x))= ?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=2x%2B1 Start with the given function.


f%28g%28x%29%29=2%28g%28x%29%29%2B1 Plug in x=g%28x%29


f%28g%28x%29%29=2%28%28x-1%29%2F2%29%2B1 Plug in g%28x%29=%28x-1%29%2F2 on the right side.


f%28g%28x%29%29=cross%282%29%28%28x-1%29%2Fcross%282%29%29%2B1 Cancel the common terms.


f%28g%28x%29%29=x-1%2B1 Simplify.


f%28g%28x%29%29=x Combine like terms.



Note: if you show that g(f(x))=x as well, then you've shown the f and g are inverse functions of each other.


If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website

Jim