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Question

The range of  function f(x) = $${x^2} + {1 \over {{x^2} + 1}}$$ is


A
[1,)
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B
[2,)
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C
[32,)
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D
None
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Solution

The correct option is A $$[1,\infty )$$
$$f\left( x \right) ={ x }^{ 2 }+\dfrac { 1 }{ { x }^{ 2 }+1 }$$
When $$ \\ x=0\\$$
$$ f\left( x \right) ={ x }^{ 2 }+\dfrac { 1 }{ { x }^{ 2 }+1 }$$
$$ \\ =0+\dfrac { 1 }{ 0+1 }$$
$$ \\ =1$$
When $$x>0$$
$$ f\left( x \right) >1$$
When $$\\ x<0$$
$$\\ f\left( x \right) >1$$
So the range of $$f(x)=[1,\infty)$$

Mathematics

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