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,

Option a is correct

Any doubts then ask

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.

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 be...