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Let f(x) be a continuous defined for `1le xle 3.` if f(x) takes rational values for all x and f(2) =10, then find the value of f(1.5)

A

20

B

5

C

10

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
We know that a continuous function defined on a closed interval attains every value between its minimum and maximum values in the interval. Therefore f(x) being continous on [1,3] will attain every value between its maximum (M) and maximum (m) values.
It is given that f(x) takes rational values for all x and have there are infinitely many irrational values between m and M. Therefore, f(x) can take rational value for all x, if f(x) has a constant rational value at all points between x=1 and x=3. In each other words,
f(x)=constant for all ` x in [1,3]`
But f(2)=10
`therefore f(x)=10 "for all "x in[1,3]`
`Rightarrow f(4)=10`
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