Function f(x) is continuous

The function f(x) is continuous in [0,1], such that f(0)=-1,
f(1/2)=1 and f(1)=-1, We can conclude that

1. f attains the value zero at least twice in [0,1]
2. f attains the value zero exactly once in [0,1]
3. f is non-zero in [0,1]
4. f attains the value zero exactly twice in [0,1]

Questions by Rujul   answers by Rujul

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contact.nidhigupta

  • Feb 19th, 2008
 

its choice 1.
Reason: Since f(x) is a continuous function and from the given data it is clear that in the range [0,1] it is changing -1 to 1 and then again -1, so f attains the value zero at least twice in [0,1].  

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Ashish.Shekhar

  • Feb 23rd, 2008
 

Another way to look at the solution would be to just draw a mental plot of the given values on x and y axis and it would be easy to see that the graph would cut the x axis twice hence two zero's

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zeptov

  • Nov 7th, 2010
 

Colloquially, "continuous" means that you can graph it without picking up your pencil. What you can't tell is whether f(x) crosses the axis lots, or just twice.

If the function were discontinuous, you'd not know whether it had to cross zero to get from -1 to 1. Consider the graph of 1/x from -1 to 1 (a discontinous function that goes from negative to positive values without ever crossing zero).

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