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Choose the correct alternative: Let f : R → R be defined by is irrationalis rationalf(x)={xx is irrational1-xx is rational then f is - Mathematics

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प्रश्न

Choose the correct alternative:

Let f : R → R be defined by `f(x) = {{:(x, x  "is irrational"),(1 - x, x  "is rational"):}` then f is

पर्याय

  • Discontinuous at x = `1/2`

  • Continuous at x = `1/2`

  • Continuous everywhere

  • Discontinuous everywhere

MCQ

उत्तर

Continuous at x = `1/2`

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Continuity
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 9: Differential Calculus - Limits and Continuity - Exercise 9.6 [पृष्ठ १३१]

APPEARS IN

सामाचीर कलवी Mathematics - Volume 1 and 2 [English] Class 11 TN Board
पाठ 9 Differential Calculus - Limits and Continuity
Exercise 9.6 | Q 22 | पृष्ठ १३१

संबंधित प्रश्‍न

Prove that f(x) = 2x2 + 3x - 5 is continuous at all points in R


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x2 cos x


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`sinx/x^2`


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Find the points of discontinuity of the function f, where `f(x) = {{:(sinx",",  0 ≤ x ≤ pi/4),(cos x",", pi/4 < x < pi/2):}`


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For what value of `alpha` is this function `f(x) = {{:((x^4 - 1)/(x - 1)",",  "if"  x ≠ 1),(alpha",",  "if"  x = 1):}` continuous at x = 1?


If f and g are continuous functions with f(3) = 5 and `lim_(x -> 3) [2f(x) - g(x)]` = 4, find g(3)


A function f is defined as follows:

`f(x) = {{:(0,  "for"  x < 0;),(x,  "for"  0 ≤ x ≤ 1;),(- x^2 +4x - 2, "for"  1 ≤ x ≤ 3;),(4 - x,  "for"  x ≥ 3):}`
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State how continuity is destroyed at x = x0 for the following graphs.


Choose the correct alternative:

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Choose the correct alternative:

At x = `3/2` the function f(x) = `|2x - 3|/(2x - 3)` is


Choose the correct alternative:

Let f be a continuous function on [2, 5]. If f takes only rational values for all x and f(3) = 12, then f(4.5) is equal to


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