Discussion Forum



1)

Let f: R→ R, g : R→ R be two functions such that f(x) = 2x - 3, g(x) = x3 + 5. The function (fog)-1(x) is equal to 

 


A) $\left(\frac{x+7}{2}\right)^{1/3}$

B) $\left(x-\frac{7}{2}\right)^{1/3}$

C) $\left(\frac{x-2}{7}\right)^{1/3}$

D) $\left(\frac{x-7}{2}\right)^{1/3}$

Answer:

Option D

Explanation:

We have, f(x) = 2x-3, g(x) = x3 + 5

(fog)x =f (x3 + 5) = 2(x3 + 5) -3 = 2x3+7

Let y= (fog)x = 2x3 + 7

$x = \left(\frac{y-7}{2}\right)^{1/3}$

(fog)-1$x = \left(\frac{x-7}{2}\right)^{1/3}$