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Let f: R->R be a continuous onto functio...

Let `f: R->R` be a continuous onto function satisfying `f(x)+f(-x)=0AAx in R`. If `f(-3)=2 \ a n d \ f(5)=4 \ i n \ [-5,5],` then the minimum number of roots of the equation `f(x)=0` is

Text Solution

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` 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 of f(x), it is clear that equation f (x) = 0 has at least three real roots.
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Knowledge Check

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