CSIR NET
Seema Asked a Question
August 27, 2020 4:05 pmpts 30 pts
  • CSIR NET
  • Mathematical Sciences

How to check uniform continuity on r

2 Let f: R R and g : la, b] > R 1. be defined as flx) =x Vx e R and glx) = * Vxe la, b]. Then : (A) f and g both are uniformly continuous (B) fis uniformly continuous and g is continuous (C) f is continuous and g is uniformly continuous (D) fand g both are continuous but not uniformly continuouus
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  • Seema
    option C is correct
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  • Shashi ranjan sinha thankyou
    However, f is not UC while g is UC....see the attachments
    • cropped2358981547513069313.jpg
    • cropped7163446465555388534.jpg
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  • Shashi ranjan sinha
    We know that polynomial functions are continuous on R, so x² is also continuous on R and hence f & g are continuous function
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