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If f(x)={((1)/(x+1)", for " 2 le x le 4)...

If `f(x)={((1)/(x+1)", for " 2 le x le 4),((x+1)/(x-3)", for " 4 lt x le 6):}` , then

A

f is discontinuous on [2, 6]

B

f is continuous on [2, 6]

C

f is continuous on [2, 6] except at `x=3`

D

f is continuous on [2, 6] except at `x=4`

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The correct Answer is:
D
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NIKITA PUBLICATION-CONTINUITY-MULTIPLE CHOICE QUESTIONS
  1. If f(x)={:{(x", for " x ge 0),(x^(2)", for " x lt 0):}, then f is

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  2. If f(x)={:{(x^(2)-4", for " 0 le x le 2),(2x+3", for " 2 lt x le 4),(x...

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  3. If f(x)={((1)/(x+1)", for " 2 le x le 4),((x+1)/(x-3)", for " 4 lt x l...

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  4. If f(x)={:{(3", if " 0 le x le 1),(4", if " 1 lt x lt 3),(5", if " 3 l...

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  5. If f(x)={:{(-2", for " x le -1),(2x", for " -1 lt x le 1),(2", for " x...

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  6. f(x)={{:(|x|+3, if x le -3),(-2x, if -3 lt x lt 3 ),(6x + 2, if x ge3)...

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  7. If f(x)={(2x", for " x lt 0),(2x+1", for " x ge 0):} , then

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  8. Function f(x)={(x-1",",x lt 2),(2x-3",", x ge 2):} is a continuous fun...

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  9. If f(x)=(x^(3)-8)/(x^(2)+x-20), then

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  10. If f(x)={:{((x^(2)-3x+2)/(x-3)", for " 0 le x lt 4),((x^(2)-1)/(x-2)",...

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  11. If f(x) is continuous at x=1, where f(x)={:{(k+x", for " x lt 1),(4x+...

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  12. If f(x) is continuous at x=0, where f(x)={:{(x^(2)+1", for " x ge 0),...

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  13. If f(x) is continuous at x=0, where f(x)={:{(k(x^(2)-2)", for " x le ...

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  14. If f(x) is continuous at x=0, where f(x)={:{(x^(2)+alpha", for " x ge...

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  15. If f(x) is continuous at x=3, where f(x)={:{((x^(2)-9)/(x-3)+alpha", ...

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  16. If f(x) is continuous at x=2 and x=10, where f(x)={:{(5", if " x le 2...

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  17. If f(x) is continuous at x=1, where f(x)={:{(kx^(2)", for " x ge 1),(...

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  18. If f(x) is continuous on [0, 8] , where f(x)={:{(x^(2)+ax+6", for " 0...

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  19. If f(x) is continuous in [0, 3], where f(x)={:{(3x-4", for " 0 le x l...

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  20. If f(x) continuous on its domain, where f(x)={:{(6", for " x le 2), (...

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