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The function defined as f(x)= _ n [ array ll ^ 2 n x & If x 0 n 1+x^n & 0 x 1 1 1+x^n & x 1 array . which of the following does not hold good

Options

  1. Acontinuous at x=0 , but discontinuous at x=1
  2. Bcontinuous at x=1 , but discontinuous at x=0
  3. Ccontinuous at both x=1 and x=0
  4. Ddiscontinuous at both x=1 and x=0

Correct answer

C. continuous at both x=1 and x=0

Step-by-step solution

aligned & f (0⁻ )=0, f (0⁺ )=1, f (0)=1 & discontinuous at x =0 & f (1⁻ )=1, f (1)=1, f (1⁺ )=0 & discontinuous at x =1 aligned

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