Q5 of 215 Page 2

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


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