Find fog (2) and gof (1) when: f: R → R; f(x) = x2 + 8 and g: R → R; g(x) = 3x3 + 1.
We have, f: R → R given by f(x) = x2 + 8 and
g : R → R given by g (x) = 3x3 + 1
fog(x) = f (g(x)) = f (3x3 + 1)
= (3x3 + 1)2 + 8
fog(2) = (3 × 8 + 1)2 + 8 = 625 + 8 = 633
Again,
gof(x) = g(f(x)) = g(x2 + 8)
= 3(x2 + 8)3 + 1
gof(1) = 3(1 + 8)3 + 1 = 2188