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AP EAMCET201921 Apr 2019Morning ShiftMathematicsFunctionsActual

Let D=R- 0,1 and f: D D, g: D D and h: D D be three functions defined by f(x)= 1 x ; g(x)=1-x and h(x)= 1 1-x . If j: D D is such that (gojof) (x)=f(x) for all x D , then which one of the following is j(x) ?

Options

  1. A(f g)(x)
  2. Bf(x)
  3. Cg(x)
  4. D(g h)(x)

Correct answer

C. g(x)

Step-by-step solution

We have, aligned & ( goj of )(x)=f(x) for all x D & g((j o f)(x))= 1 x & 1-(j o f)(x)= 1 x & 1-j(f(x))= 1 x & 1-j ( 1 x )= 1 x & j ( 1 x )=1- 1 x & j(x)=1-x=g(x) aligned

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