1. Tardigrade
  2. Question
  3. Mathematics
  4. The number of integral values of x satisfying the equation operatornamesgn([(15/1+x2)])=[1+ 2 x ] is [Note: operatornamesgn( y ),[ y ] and y denote signum function, greatest integer function and fractional part function respectively.]

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Q. The number of integral values of $x$ satisfying the equation $\operatorname{sgn}\left(\left[\frac{15}{1+x^2}\right]\right)=[1+\{2 x\}]$ is
[Note: $\operatorname{sgn}( y ),[ y ]$ and $\{ y \}$ denote signum function, greatest integer function and fractional part function respectively.]

Relations and Functions - Part 2

Solution:

$\operatorname{sgn}\left(\left[\frac{15}{1+x^2}\right]\right)=1$
$1+x^2 \leq 15 \Rightarrow x^2 \leq 14$
$\therefore$ Number of integral values of $x$ are 7