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If f(x)={:{((x^(2)-9)/(x-3)", for " 0 lt...

If `f(x)={:{((x^(2)-9)/(x-3)", for " 0 lt x lt 3),(x+3", for " 3 le x lt 6),((x^(2)-9)/(x+3)", for " 6 le x lt 9):}`, then f is

A

continuous at `x=3, x=6`

B

discontinuous at `x=3, x=6`

C

continuous at `x=6` and discontinuous at `x=3`

D

continuous at `x=3` and discontinuous at `x=6`

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Verified by Experts

The correct Answer is:
D
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NIKITA PUBLICATION-CONTINUITY-MULTIPLE CHOICE QUESTIONS
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  3. If f(x)={:{((x^(2)-9)/(x-3)", for " 0 lt x lt 3),(x+3", for " 3 le x l...

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  4. If f(x)={:{((sin 2x)/(sqrt(1-cos 2x))", for " 0 lt x lt pi/2),((cos x)...

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  12. If f(x)=sqrt(x-2), for 2 lt x lt 4, then f(x) is

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  13. If f(x)={:{(1-x", for " 0 lt x le 1), ( 1/2 ", for " x=0):}, then in [...

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  14. If f(x)={:{(3x+5", for " 0 le x lt 3),(2x+8", for " 3 le x lt 5),(x+13...

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  15. If f(x)={:{((sinx)/(x)", for " x lt 0),(x+1", for " x ge 0):}, then

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  17. If f(x)={:{((sin2x)/(sqrt(1-cos2x))", for " 0 lt x le pi/2),((cos x)/(...

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  18. If f(x)={:{(x", for " 0 le x lt 1),(2", for " x=1),(x+1", for " 1 lt x...

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  19. If f(x)=(x^(3)+3x+5)/(x^(3)-3x+2) in [0, 5], then f is

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