If fx 6 x 2x2 then find and simplify fx f1x 1Solutionfx

If f(x) = 6 + x - 2x^2, then find and simplify f(x) - f(-1)/x - (-1)

Solution

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

f(-1) = 6 + (-1) - 2(-1)^2 = 6 - 1 - 2 = 3

{f(x) - f(-1)} / x - (-1)

= { 6 + x - 2x^2 - 3 } / ( x + 1 )

= ( -2x^2 + x + 3 ) / ( x+1)

factoring the numerator

-(x+1) (2x-3) / (x+1)

= - (2x - 3 )