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The function f(x)={{:(,3x-1,"if "x lt 1)...

The function `f(x)={{:(,3x-1,"if "x lt 1),(,x^(2),"if "x gt 2):}}` is continous

A

`(-oo,1)`

B

`(2,oo)`

C

`(-oo,1) cup (2,oo)`

D

(1,2)

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The correct Answer is:
C
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DIPTI PUBLICATION ( AP EAMET)-LIMITS AND CONTINUITY-Exercise 1C(Continuity)
  1. f(x)=1 for x is rational f(x)=-1 for x irrational, f is continuous on

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  2. If a lt b then f(x) =sqrt ((x-a)/(b-x)) is continuous on

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  3. The function f(x)={{:(,3x-1,"if "x lt 1),(,x^(2),"if "x gt 2):}} is co...

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  4. If f: RR to RR is defined by f(x)={{:(,(x+2)/(x^(2)+3x+2),"if "x in R-...

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  5. Let 'f' be a non-zero real valued continuous function satisfying f(x ...

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  6. If f(x+y)=f(x) f(y) and f(x)=1+g(x), h(x)" where "underset(x to 0)"Lt"...

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  7. Let f(x)=f(x) f(y) for all x and y. If f(x) is continuous at x=1. then...

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  8. A discontinuous function y=f(x) satisfying x^(2)+y^(2)=4" is given by ...

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  9. The discontinuous points of f(x)=(1)/(log |x|)" are "

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  10. If f : R to R is defind by f (x) = x - [x], where [x] , is the gr...

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  11. If f : R to R is a continuous defined by f(x)=[x]cos ((2x-1)/(2))pi, w...

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  12. f(x)=sqrt(x-[x]) is discontinuous at

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  13. The value of f(0) so that f(x)=(1+x)^(5//x) is continuous at x=0 is

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  14. The value of f(0) so that f(x)=(sin x)/(x) is continuous at x=0 is

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  15. The value of f(0) so that f(x)=(3x+4 tan x)/(x) is continuous at x=3 i...

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  16. The value of f(0) so that f(x)=(3x+4 tan x)/(x) is continuous at x=0 i...

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  17. The value of f(0) so that f(x)=(sqrt(1+x)-1)/(x) is continuous at x=0 ...

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  18. If f(x)=x^(1/(x-1))" for "x ne 1 and if f is continuous at x=1 then f(...

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  19. The value of f(0) so that the function f(x)=((27-2x)^(1//3)-3)/(9-3(24...

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  20. In order that the function f(x)=(x+1)^(cot x) is continous at x=0, f(0...

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