Question

If f : R → R, f(x) = 2x + 1 and g : R → R, g(x) = x³, then (gof)^-1(27) is equal to :

(a) 2

(b) 1

(c) -1

(d) 0

Answer 1

Answer is (b)

Let (gof)^-1(27) = x

∴ (gof)(x) = 27

g{f(x)} = 27

g{2x + 1} = 27

(2x + 1)³ = 27

2x + 1 = 27^1/3

2x + 1 = 3^{3 x 1/3}

2x + 1 = 3

∴ 2x = 2

x = 1