Question 588897: I need help solving this math problem. Can you help me solve? Thank you.
If f(x) = 2x - x² + 1, find f(x-3)
Answer by Edwin McCravy(20054)   (Show Source):
You can put this solution on YOUR website! If f(x) = 2x - x² + 1, find f(x-3)
f(x) = 2x - x² + 1
Replace all the x's by an open pair of parentheses, ( )'s
f(( )) = 2( ) - ( )² + 1
Open all the ( )'s a little wider:
f(( )) = 2( ) - ( )² + 1
Place x-3 between each set of parentheses
f((x-3)) = 2(x-3) - (x-3)² + 1
Erase the redundant parentheses inside f((x-3)) and make it f(x-3)
f(x-3) = 2(x-3) - (x-3)² + 1
Leave the left side as it is, but simplify the right side:
f(x-3) = (2x-6) - (x-3)(x-3) + 1
f(x-3) = (2x-6) - (x²-6x+9) + 1
f(x-3) = 2x - 6 - x² + 6x - 9 + 1
f(x-3) = 8x - 14 - x²
That's the answer, or maybe you'd like to arrange it in
descending order:
f(x-3) = -x² + 8x - 14
Edwin
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