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BITSAT2024MathematicsFunctionsActual

f(x)= x+ x, g(x)=x^2-1 , then g(f(x)) is invertible if

Options

  1. A- 4 x 4
  2. B- 2 x 0
  3. C- 2 x
  4. D0 x 2

Correct answer

A. - 4 x 4

Step-by-step solution

Given that, f(x)= x+ xg(x)=x^2-1g[f(x)]=( x+ x)^2-1= ^2 x+ ^2 x+2 x x-1=1+ 2 x-1= 2 x ( ^2 x+ ^2 x=1, x=2 x x ) Among the given options, 2 x is monotonous (here strictly increasing) in - 4 x 4 . So, g(f(x)) is invertible in - 4 x 4 .

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