Question

2. If f:R → R is given by f(x) = x^2 - 2x - 3 and g:R → R is given by g(x) = 3x - 4, then find (gof)(x) and (fog)(x).​

Answer 1

fog:R → R and gof:R → R f(x) = x2 + 2x – 3 and g(x) = 3x – 4 Now, gof(x)=g(f(x))= g(x2 + 2x – 3) gof(x) = 3(x2 + 2x–3) – 4 ⇒ gof(x)= 3x2 + 6x – 9 – 4 ⇒ gof(x) = 3x2 + 6x – 13 and, fog= f(g(x)) = f(3x – 4) fog(x) = (3x – 4)2 + 2(3x – 4) – 3 = 9x2 + 16 – 24x + 6x – 8 – 3 ∴ fog(x) = 9x2 – 18x + 5 Thus, gof(x) = 3x2 + 6x – 13 and fog(x) = 9x2 – 18x + 5Read more on Sarthaks.com - https://www.sarthaks.com/1032659/find-gof-and-fog-when-f-rr-and-g-rr-is-defined-by-f-x-x-2-2x-3-and-g-x-3x-4