Given fx x2 2x 3 gx x 1 find fgx find fgxSolutionGiven t

Given f(x) = x^2 - 2x - 3: g(x) x + 1 find (fg)(x) find (f/g)(x)

Solution

Given that

f(x) = x² - 2x - 3 , g(x) = x + 1

9 ) (fg)(x) = f(x).g(x)

= (x² - 2x - 3)(x + 1)

= x³ + x² -2x² - 2x - 3x - 3

(fg)(x) = x³ - x² - 5x - 3

10 ) Given that

(f/g)(x) = f(x)/g(x)

=  (x² - 2x - 3)/(x + 1)

= [ (x - 3)(x + 1) ] /(x + 1) [ since , x² - 2x - 3 = x² - 3x + x - 3 = x(x - 3) + 1(x-3) = (x-3)(x+1) ]

(f/g)(x) = x - 3