Divam Kumar posted an Question
September 09, 2020 • 01:49 am 30 points
  • IIT JAM
  • Mathematics (MA)

Let f:rr be a continuous function satisfying x+ f0)dt me"-1 for all xe r. then the set (xe r: 1sf)s2) is the interval (a) log 2, log 3) c)le-1.e-) (b) (2log 2,

Let f:RR be a continuous function satisfying x+ f0)dt me"-1 for all xe R. Then the set (xe R: 1sf)s2) is the interval (A) log 2, log 3) C)le-1.e-) (B) (2log 2, 3log 3 (D) [0, e1

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    Jagat Chaudhary

    use leibnitz to differentiate both sides of given expression. hence we get 1+ f(x)= e^x hence f(x)=e^x - 1 now use this f(x) in given inequality ans solve inequality as shown below. 1≤e^x-1≤2 2≤e^x≤3 take log both sides hence x€ [ log2 , log3] option (A)

  • Srinath

    Apply Leibniz rule, for differentiating under the integral. Find the inverse of f(x). You'll see that the answer is option A. If you have doubts, ask.

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