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Question

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


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 C $$[1\infty)$$
Given, $$f(x)=x^2+\dfrac{1}{x^2+1}$$.
Since $$x^2\ge 0$$.
Now, $$x^2\ge0, f(x)\ge1$$ or $$f(x)\in [1,\infty)$$.

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