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Let $\mathrm{R}$ be the set of real numbers and $\mathrm{f}: \mathrm{R} \rightarrow \mathrm{R}$ be given by $\mathrm{f}(\mathrm{x})=\sqrt{|\mathrm{x}|}-\log (1+|\mathrm{x}|)$. We now make the following assertions:
I. There exists a real number $\mathrm{A}$ such that $\mathrm{f}(\mathrm{x}) \leq \mathrm{A}$ for all $x$
II. There exists a real number $B$ such that $f(x) \geq B$ for all $x$
Options:
I. There exists a real number $\mathrm{A}$ such that $\mathrm{f}(\mathrm{x}) \leq \mathrm{A}$ for all $x$
II. There exists a real number $B$ such that $f(x) \geq B$ for all $x$
Solution:
1133 Upvotes
Verified Answer
The correct answer is:
I is false and II is true
graph of given function actually look like this
Clear from graph option (B) is right.
Clear from graph option (B) is right.
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