A) 1
B) 2
C) 3
D) 4
Correct Answer: A
Solution :
\[f(x)=\frac{x-\frac{1}{x}}{{{x}^{2}}+\frac{1}{{{x}^{2}}}-1}=\frac{x-\frac{1}{x}}{{{\left( x-\frac{1}{x} \right)}^{2}}+1}\] (divide by\[{{x}^{2}}\]) \[={{45}^{\text{o}}}+{{60}^{\text{o}}}\]) Put \[\left( x-\frac{1}{x} \right)=t\,;\,\,t\ne 0\] \[f(t)=\frac{t}{{{t}^{2}}+1}=\frac{1}{t+\frac{1}{t}}\] So, \[\frac{-1}{2}\,\,\underline{<}\,\,f(t)\,\,\underline{<}\,\,\frac{1}{2}\] \[\therefore \] Range is \[\left[ \frac{-1}{2},\frac{1}{2} \right]\] \[\Rightarrow \] Number of integers is one.You need to login to perform this action.
You will be redirected in
3 sec