Question

The function f(x) is continuous for all x∈R. It is known that equation f(x)=1 has 100 solutions, and equation f(x)=−1 has 200 solutions. What is the smallest number of solutions that the equation f(x)=0 can have?

Answer 1

1

Explanation:

You want to know the smallest number of solutions for continuous function f(x) = 0 if we have 100 solutions for f(x) = 1 and 200 solutions for f(x) = -1.

Solutions

The attached graph shows such a function with exactly 1 solution for f(x) = 0.

The minimum number of solutions is 1.

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Additional comment

The Intermediate Value Theorem tells you that if f(a) = 1 and f(b) = -1, there exists at least one value c between 'a' and 'b' such that f(c) = 0. The minimum number of zero-crossings is 1.

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