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Letf : R to Rbe a continuous onto function satisfying f(x)+f(-x) = 0, forall x in R . Iff(-3) = 2 and f(5) = 4in [-5, 5], then what is the minimum number of roots of the equation f(x) = 0? |
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Answer» Solution :` f(x)+ f(-x) = 0` f(x) is an odd function. Since the points (-3, 2) and (5, 4) LIE on the curve, (3, -2) and (-5, -4) will also lie on the curve. For minimum number of roots, graph of the continuous function f(x) is as FOLLOWS. From the above graph off(x), it is clear that equation f (x) = 0 has at least three real roots. |
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