Find gof and fog when f: R → R and g: R → R is defined by
f(x) = x2 + 2x – 3 and g(x) = 3x – 4
Since, f:R → R and g:R → R
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 + 5