Mathematics · Real Analysis
Let f: R → R be a function. Then which of the following statements is FALSE?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1The set of zeroes of a continuous function on R is a closed set.
- 2If 'f' is continuous and bounded, then 'f' has a fixed point.
- 3There exists a function 'f' such that f(x + y) = f(x).f(y) for all x, y ∈ R and f(0) = 2.✓
- 4If f is periodic and limx→∞ f(x) = a, then 'f' is a constant function.
Correct answer
There exists a function 'f' such that f(x + y) = f(x).f(y) for all x, y ∈ R and f(0) = 2.
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