Search any question & find its solution
Question:
Answered & Verified by Expert
Let $f:[-2,2] \rightarrow R$ be a continuous function such that $f(x)$ assumes only irrational values. If $f(\sqrt{2})=\sqrt{2},$ then
Options:
Solution:
2485 Upvotes
Verified Answer
The correct answer is:
$f(\sqrt{2}-1)=\sqrt{2}$
If a function $f(x)$ assumes only irrational values which is also continuous, then $f(x)$ must be constant function.
$\Rightarrow \quad f(x)=\sqrt{2}$
$$
[\because f(\sqrt{2})=\sqrt{2} \mid
$$
$\therefore \quad f(\sqrt{2}-1)=\sqrt{2}$
$\Rightarrow \quad f(x)=\sqrt{2}$
$$
[\because f(\sqrt{2})=\sqrt{2} \mid
$$
$\therefore \quad f(\sqrt{2}-1)=\sqrt{2}$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.