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