SOLUTION: I am coming up with -x^2+5x-7 for this problem Given f (x) = 5x - 4 and g (x) = x2 + 3, find (g - f )(x). Simplify when possible. But that is not one of the choices. Can you

Question 1195941: I am coming up with -x^2+5x-7 for this problem
Given f (x) = 5x - 4 and g (x) = x2 + 3, find (g - f )(x). Simplify when possible.
But that is not one of the choices. Can you please help me?
Found 2 solutions by Alan3354, math_tutor2020:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
I am coming up with -x^2+5x-7 for this problem
Given f (x) = 5x - 4 and g (x) = x2 + 3, find (g - f )(x)
-------------------------
Show how you got your result.
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

It looks like you may have computed (f - g)(x) instead of (g - f)(x)
The order matters since the two expressions are slightly different.

It's the same idea as to why something like 10-4 = 6 and 4-10 = -6 are slightly different (same absolute value, but the results differ in sign)

This is what (f-g)(x) looks like
(f - g)(x) = f(x) - g(x)
(f - g)(x) = [ f(x) ] - [ g(x) ]
(f - g)(x) = [ 5x-4 ] - [ x^2+3 ]
(f - g)(x) = 5x-4 - x^2-3
(f - g)(x) = -x^2 + 5x - 7
and it matches what you got.

However, this is what the steps and answer should be
(g - f)(x) = g(x) - f(x)
(g - f)(x) = [ g(x) ] - [ f(x) ]
(g - f)(x) = [ x^2+3 ] - [ 5x-4 ]
(g - f)(x) = x^2+3 - 5x+4
(g - f)(x) = x^2 - 5x + 7

The subtle difference between (f - g)(x) and (g - f)(x) is that each term has a sign flip.
Eg: we go from +5x in (f - g)(x) to -5x in (g - f)(x)
Put another way, (f - g)(x) = -1*(g - f)(x)

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