A) \[(-1,1)-\{0\}\]
B) \[R-[-1,1]\]
C) \[\left[ -\frac{1}{2},\frac{1}{2} \right]\]
D) \[R-\left[ -\frac{1}{2},\frac{1}{2} \right]\]
Correct Answer: C
Solution :
Here, f(x) is an odd function and f(0) = 0 Now, when \[x>0,f(x)=\frac{1}{x+\frac{1}{x}}\in \left( 0,\frac{1}{2} \right]\] When \[x<0,f(x)=\frac{1}{x+\frac{1}{x}}\in \left[ -\frac{1}{2},0 \right)\] \[\therefore \]Range of f(x) is \[\left[ -\frac{1}{2},\frac{1}{2} \right].\]You need to login to perform this action.
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