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.]

Question

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.] (A) 5 (B) 7 (C) 15 (D) 16

Tardigrade Admin · Accepted Answer

operatornamesgn([(15/1+x2)])=1 1+x2 ≤ 15 ⇒ x2 ≤ 14 ∴ Number of integral values of x are 7

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

5

7

15

16

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

Q. The number of integral values of x satisfying the equation sgn([1+x215​])=[1+{2x}] is [Note: sgn(y),[y] and {y} denote signum function, greatest integer function and fractional part function respectively.]

5

7

15

16

sgn([1+x215​])=1 1+x2≤15⇒x2≤14 ∴ Number of integral values of x are 7

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

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