Let f-1-10- - Q be a continuous function and f 1 - 10- then f 10 is equal to

The correct option is D 10 As function is a continuous function as given in the #10;question and range of f(x) is only rational numbers and hence, funct ...

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Standard XII

Mathematics

Definition of Functions

Let f:[1,10...

Question

Let $f : [1, 10] \to Q$ be a continuous function and $f (1) = 10,$ then $f (10)$ is equal to

\frac{1}{10}

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Solution

The correct option is D $10$
As function is a continuous function as given in the question and range of f(x) is only rational numbers and hence, function must be a constant function otherwise if the value of f(x) increases or decreases then at some point f(x) will have irrational value between any two rational values due to its continuity.

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Let f:[1,10]→Q be a continuous function and f(1)=10, then f(10) is equal to

Let $f : [1, 10] \to Q$ be a continuous function and $f (1) = 10,$ then $f (10)$ is equal to