Question

# The range of the function $$f\left( x \right) ={ x }^{ 2 }+\dfrac { 1 }{ { x }^{ 2 }+1 }$$

A
(1,+)
B
(2,+)
C
(32+)
D
none of these

Solution

## The correct option is A $$\left(1,+\infty\right)$$$$f(x)=x^{2}+\dfrac{1}{x^{2}+1}$$ Range of $$x^{2}=[0, \infty)$$ Range of $$\frac{1}{x^{2}+1}=[0,1]$$ Now, putting the value common in above both, Range of $$f(x)=(1, \infty)$$Mathematics

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