Improper Range

Algebra Level 3

Range of the function f ( x ) = x 2 + x + 1 x 2 + 1 f(x)=\frac{x^{2}+x+1}{x^{2}+1} is?

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( 1 2 , 3 2 ) \left(\frac{1}{2},\frac{3}{2}\right) ( 0 , 3 ) (0,3) [ 0 , 3 ] [0,3] [ 1 2 , 3 2 ] \left[\frac{1}{2},\frac{3}{2} \right]

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