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AP EAMCET202422 May 2024Evening ShiftMathematicsFunctionsActual

Define the functions f, g and h from R to R such that f(x)=x^2-1, g(x)= x^2+1 and h(x)= array l 0, if x 0 x, if x 0 array . consider the following statements

Options

  1. Afog is invertible
  2. Bh is an identify function
  3. Cfog is not invertible
  4. D(h f g) x=x^2

Correct answer

C. fog is not invertible

Step-by-step solution

f g(x)=f ( x^2+1 )= (x^2+1 )-1=x^2 Codomain of fog (x)= R and Range of fog (x)=[0, ) fog is not onto function fog is not invertible. Now (h f g) x=h [f g(x)]=h (x^2 ) x^2 0 x R . Hence, (h fog )(x)=x^2 also given, h(x)= array ll 0, & if x 0 x, & if x 0 array . is not identity function because for x 0, h(x) x

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