This is a Test of Mathematics Solution Subjective 75 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance.

Also visit: I.S.I. & C.M.I. Entrance Course of Cheenta

## Problem

Show that there is at least one value of for which

## Solution

is a continuous function. Now if we can chose takes both negative & positive numbers then the have a solution.

For , & for , .

So by intermediate value theorem we can say that has a solution for some real .