Question 588897
If f(x) = 2x - x² + 1, find f(x-3)
<pre>
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