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Manipal MET2014MathematicsFunctions

Let f: R R be defined by f(x)= x 1+x^2 , then (f f f)(x) is

Options

  1. Ax 1+x^2
  2. Bx 1+3 x^2
  3. Cx
  4. D1

Correct answer

B. x 1+3 x^2

Step-by-step solution

Given, f(x)= x 1+x^2 aligned (f f) x & = f(f(x)) & =f ( x 1+x^2 )= x 1+x^2 1+ x^2 1+x^2 aligned ( fof ) x= x 1+2 x^2 Now, (fofo) (x)=f (f f) x x=f ( x 1+2 x^2 )= x 1+2 x^2 1+ x^2 1+2 x^2 = x 1+3 x^2

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