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  • Let   be a continuous function defined for <img alt="\mathrm{1 \leq x \leq 3}" src="/latex-image/?%5Cmathrm%7B1%20%5

Let \mathrm{f(x)}  be a continuous function defined for \mathrm{1 \leq x \leq 3}. If \mathrm{f(x)} takes rational values for all \mathrm{x} and \mathrm{f(2)=10}  then the value of \mathrm{f(1.5)} is

Option: 1

7.5


Option: 2

10


Option: 3

5


Option: 4

infinite


Answers (1)

As \mathrm{f(x)}  is continuous in \mathrm{[1,3], f(x)} will attain all values between \mathrm{f(1)} and \mathrm{f(3)}. As \mathrm{f(x)} takes rational values for all \mathrm{x} and there are innumerable irrational values between \mathrm{f(1)} and \mathrm{f(3)}, \mathrm{f(x)} can take rational values for all \mathrm{x} if \mathrm{f(x)} has a constant rational value at all points between \mathrm{x=1} and \mathrm{x=3}. So, \mathrm{f(2)=f(1.5)=10.}

Posted by

Ramraj Saini

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