Consider the function $f : ( - \infty , \infty ) \rightarrow ( - \infty , \infty )$ defined by $$f ( x ) = \frac { x ^ { 2 } - a x + 1 } { x ^ { 2 } + a x + 1 } , 0 < a < 2 .$$ Which of the following is true? (A) $f ( x )$ is decreasing on $( - 1,1 )$ and has a local minimum at $x = 1$ (B) $f ( x )$ is increasing on $( - 1,1 )$ and has a local maximum at $x = 1$ (C) $f ( x )$ is increasing on $( - 1,1 )$ but has neither a local maximum nor a local minimum at $x = 1$ (D) $f ( x )$ is decreasing on $( - 1,1 )$ but has neither a local maximum nor a local minimum at $x = 1$
Consider the function $f : ( - \infty , \infty ) \rightarrow ( - \infty , \infty )$ defined by
$$f ( x ) = \frac { x ^ { 2 } - a x + 1 } { x ^ { 2 } + a x + 1 } , 0 < a < 2 .$$
Which of the following is true?\\
(A) $f ( x )$ is decreasing on $( - 1,1 )$ and has a local minimum at $x = 1$\\
(B) $f ( x )$ is increasing on $( - 1,1 )$ and has a local maximum at $x = 1$\\
(C) $f ( x )$ is increasing on $( - 1,1 )$ but has neither a local maximum nor a local minimum at $x = 1$\\
(D) $f ( x )$ is decreasing on $( - 1,1 )$ but has neither a local maximum nor a local minimum at $x = 1$