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Standard XII

Mathematics

Greatest Integer Function

Suppose that ...

Question

Suppose that $f (\frac{1}{2}) = 1$ and f is continuous on $[0, 1]$ assuming only rational value in the entire interval. The number of such function is :

infinite

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2

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4

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1

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Solution

The correct option is D $1$
Given: $f (\frac{1}{2}) = 1$ and f is continous on $[0, 1]$ and only rational value is in the entire interval
To find: number of such functions
Sol: f is continous and only rational value is in the interval $[0, 1]$
Also $f (\frac{1}{2}) = 1$
This is possible only if $f (x) = 1$ for $x \in [0, 1]$
In all other cases if $f (x)$ it will definitely take infinitely many irrational values in $[0, 1]$

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Similar questions

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Suppose that f(12)=1 and f is continuous on [0,1] assuming only rational value in the entire interval. The number of such function is :

Suppose that $f (\frac{1}{2}) = 1$ and f is continuous on $[0, 1]$ assuming only rational value in the entire interval. The number of such function is :