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Manipal MET2011MathematicsContinuity and Differentiability

The value of f(0) , so that the function f(x)= 2-(256-7 x)^ 1 / 8 (5 x+3 x)^ 1 / 5 -2 , x 0 is continuous everywhere is given by

Options

  1. A-1
  2. B1
  3. C2^6
  4. DNone of these

Correct answer

D. None of these

Step-by-step solution

For f(x) to be continuous everywhere, we must have aligned f(0) & = _ x 0 f(x) & = _ x 0 2-(256-7 x)^ 1 / 8 (5 x+32)^ 1 / 5 -2 & = _ x 0 7 8 (256-7 x)^ -7 / 8 (5 x+32)^ -4 / 5 & = 7 8 2⁻⁷ 2⁻⁴ = 7 64 aligned

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