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Manipal MET2018MathematicsContinuity and Differentiability

If f(x)= array ll x^2-9 x-3 , & if x 3 2 x+k, & otherwise array . is continuous at x=3 , then k is equal to

Options

  1. A3
  2. B0
  3. C-6
  4. D1/6

Correct answer

B. 0

Step-by-step solution

Since, f(x) is continuous at x=3 , then _ x 3 f(x)=f(3) ...(i) aligned & _ x 3 x^2-9 x-3 = _ x 3 x+3=3+3=6 & and f(3)=2 3+k=k+6 aligned From Eq. (i), 6=k+6 k=0

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