Question

g : R→R, g(x) = 3 + cube√x and f(g(x)) = 2 - cube√x + x then f(x) =....

(a) x3 - x2 + x - 5

(b) x3 - 9x2 + 26x + 22

(c) x3 + 9x2 - 26x + 5

(d) x3 + x2 - x + 5

Answer 1

The correct option (b) x3 - 9x2 + 26x + 22

Explanation:

f(3 + 3√x) = 2 – 3√x + x now take 3 + 3√x = y

then x = (y – 3)3 and 3√x = y – 3

∴ f(y) = 2 – (y – 3) + (y – 3)3