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Question

Let f:RR,g:RR, be two functions,  such that f(x) =2x – 3, g (x) = x3 + 5.
The function (fog)1 (x) is equal to
 
  1. (x72)13
  2. (x72)13
  3. (x+72)13
  4. (x27)13


Solution

The correct option is B (x72)13
We have, f : R R, g: R R defined by f(x) = 2x - 3 and g (x) = x3 + 5
It can be checked that f(x) and g(x) are bijective functions
fo g is also bijective and (fog) = f(g(x)) = f (x3+5)=2(x3+5)3=2x3+7
(fog)(x)=y2x3+7=yx=(y72)13
 (fog)1(x)=(x72)13,x ϵ R
The correct answer is (d).

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