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###### Jinesh Jain posted an Question
February 08, 2022 • 00:22 am 30 points
• IIT JAM
• Mathematics (MA)

# Let f: rr be defined by f(x)=f]. 9. 14. let f:0,1> r be the points of discontinuity of f are the continuous (a.) only the integral points tunction defined by f(

Let f: RR be defined by f(x)=F]. 9. 14. Let f:0,1> R be The points of discontinuity of f are the continuous (a.) Only the integral points Tunction defined by f(x) =)-2) x-3)(x-4) .Then the maximal subset of R on which b.) All rational numbers (c.) {tn :n is a non-negative integer} f has a continuous extension is (d.) All real numbers (a.)-,3) 10. A monotonic function (a.) Is always continuous (b.)-,3)u(4,o) (b.) Is continuous only if it intermediate value property (c.) R\{3,4 (d.) R (c.) Can be nowhere continuous (d.) Can be discontinuous at finitely many 15. The Continuous function f:R>R points defined by f(x) = (+1)is Which one of the following functions has exactly two points of discontinuity? 11. (a.) Onto but not one-one (b.) One-one but not onto (a.) fG)=if x>0 (a.) f(x)=o if xs0 (c.) Both one-one and onto (d.) Neither one-one nor onto 1 if 0Sxsl (b.) fx)0 otherwise 16. Let f:R >R be a continuous function. If fOCN, then xif 0srsl (c.) fx)10 otherwise (a.) f(R) =N (b.) f(R)CN but f need not be constant (d.) f(x)= 1if r is rational 0 if xis irational (C.) f is unbounded 12 Let f:a, b R be a continuous function (d.) f is a constant function and let f (a) < f(b). Then by intermediate Let f:la,b]> R be a monotonic function. 17. value theorem Then (a.) fla, b]) =[f (a). ftb)] (a.) f is continuous (b.) s(la. b]) =[sla). f(b)] (b.) f is discontinuous at at most two points (c.) f([a, b) c[s(a), f (b)] (c.) f is discontinuous at at finitely many (d.) f([a, b]) + [f (a). f (b)] points 13. (d.) f is discontinuous at at most countable Consider the function f:R R defined if x is rational, points Let S by f(x)= 2x-1, if x is irrational Let f: 0 10) >[0,10 be a continuous 18. be the set of points where f is continuous. Then mapping. Then (a.) f need not have any fixed point (a.) S = {1} (b.) f has at least 10 fixed points b.) S = {-1} (c.) f has at least 9 fixed points (c.) S=1,1} (d.) f has at least one fixed point (d.) S = o IIT Khas, Near I.LT., New Delhi-110016, Ph.: (011)-26537527, Cell: 9999183434 & 9899161734, 8588844789 udomy com: Website: www.dipsacademv.com 178

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• ##### Anonymous User Best Answer

9. f(x)=[x] is discontinue at x=n for all n€Z so f(x)=[x²] is discontinue at x²=n=> x=±√n for all n€N 10 monotonic fun always continus 11 b f is discontinus at 0,1 bcz f(0+)=1 f(0-)=0 and f(1+)=0 f(1-)=1

sir, will you please send the solutions of question no. 12, 14, 15, 16, 17, 18

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