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Let f : RRtoRR be defined by f(x)={{:(x"...

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

A

discontinuous at `x=1/2`

B

continuous at `x=1/2`

C

continuous everywhere

D

discontinuous everywhere

Text Solution

Verified by Experts

The correct Answer is:
B
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PREMIERS PUBLISHERS-DIFFERENTIAL CALCULUS LIMITS AND CONTINUITY-SOLUTION TO EXERCISE 9.6
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  2. Choose the correct or the most suitable answer from the given four alt...

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  3. Choose the correct or the most suitable answer from the given four alt...

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  4. If f(x)=x(-1)[1/x]xle0, then the value of lim(xto0)f(x) is equal to

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  5. Choose the correct or the most suitable answer from the given four alt...

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  6. Let the function f be defined by f(x)={(3x0lexle1),(-3x+51ltxle2):}, t...

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  7. If f:R rarr R is defined by f(x)= floor(x-3)+|x+4| for xepsilonR,then ...

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  8. lim(xrarr0)(xe^x -sin2x)/x is :

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  9. If lim(xto0)(sinpx)/(tan3x)=4, then the value of p is

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  10. lim(alphato pi/4)(sinalpha-cosalpha)/(alpha-pi/4) is

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  11. Choose the correct or the most suitable answer from the given four alt...

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  12. Choose the correct or the most suitable answer from the given four alt...

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  13. lim(xto0)(e^(tanx)-e^(x))/(tanx-x)=

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  14. The value of lim(xto0)sinx/sqrtx is

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  15. The value of lim(xtok^(-))x-[x], where k is an integer

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

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  17. Let f : RRtoRR be defined by f(x)={{:(x" "x" is irrational"),(1...

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  18. The function f(x)={{:((x^(2)-1)/(x^(3)+1)" "xne1),(P" "x=-1):} is...

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  19. Let f be a continuous function on [2, 5]. If f takes only rational val...

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  20. Let a function f be defined by f (x) =[x-|x|]/x for xne 0 and f(0)=2.T...

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