Question

Let f(x) = 3x2 + x − 3 and g(x) = x2 − 5x + 1. Find f(x) − g(x).

Answer 1

Answer: 2x^2 + 6x - 4

Proof of validity is shown below.

Answer 2

Answer: 2x^2 + 6x - 4

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Work Shown:

f(x) - g(x) = [ f(x) ] - [ g(x) ]

f(x) - g(x) = ( 3x^2+x-3) - ( x^2-5x+1 )

f(x) - g(x) = 3x^2+x-3 - x^2+5x-1

f(x) - g(x) = (3x^2-x^2) + (x+5x) + (-3-1)

f(x) - g(x) = 2x^2 + 6x - 4