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.
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Show that there is at least one value of for which
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 .