SOLUTION: Given the functions f(x) = -x2 + 2x + 3 and g(x) = (x-2)2, find g(f(x)). Simplify to remove all parentheses. thanks for all the help!

Algebra ->  Rational-functions -> SOLUTION: Given the functions f(x) = -x2 + 2x + 3 and g(x) = (x-2)2, find g(f(x)). Simplify to remove all parentheses. thanks for all the help!      Log On


   

Question 135260: Given the functions f(x) = -x2 + 2x + 3 and g(x) = (x-2)2, find g(f(x)). Simplify to remove all parentheses.
thanks for all the help!
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
I'm presuming that you meant: f%28x%29+=+-x%5E2+%2B+2x+%2B+3 and g%28x%29+=+%28x-2%29%5E2

g%28f%28x%29%29=%28%28f%28x%29%29-2%29%5E2=%28f%28x%29%29%5E2-4%28f%28x%29%29%2B4

Just substitute -x%5E2+%2B+2x+%2B+3 everywhere you see f%28x%29 in %28f%28x%29%29%5E2-4%28f%28x%29%29%2B4 and start multiplying. Take care with your signs. Remember a minus sign distributes across parentheses when you remove any parentheses. Collect your like terms and you are done.