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MHT CET202310 May 2023Evening ShiftMathematicsFunctionsActual

Let f (x)= e ^x-x and g (x)=x^2-x, x R , then the set of all x R , where the function h (x)=( fog )(x) is increasing is

Options

  1. A[0, 1 2 ] [1, )
  2. B[-1,- 1 2 ] [ 1 2 , )
  3. C[0, )
  4. D[- 1 2 , 0 ] [1, )

Correct answer

A. [0, 1 2 ] [1, )

Step-by-step solution

aligned & h (x)=( fog )(x) & h (x)= f (x^2-x ) & h (x)= e ^ x^2-x -x^2+x & h ^ (x)= e ^ x^2-x (2 x-1)-2 x+1 & h ^ (x)= ( e ^ x^2-x -1 )(2 x-1) aligned For function h (x) to be increasing, aligned & h ^ (x) 0 & ( e ^ x^2-x -1 )(2 x-1) 0 & x [0, 1 2 ] [1, ) aligned array c|c|c|c h ^ - & + & - & + & & & 0 & 1 2 & 1 array

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