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Question

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


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