Consider the function f:(-oo,oo)vec(-oo,...

Consider the function `f:(-oo,oo)vec(-oo,oo)` defined by `f(x)=(x^2+a)/(x^2+a),a >0,` which of the following is not true? maximum value of `f` is not attained even though `f` is bounded. `f(x)` is increasing on `(0,oo)` and has minimum at `,=0` `f(x)` is decreasing on `(-oo,0)` and has minimum at `x=0.` `f(x)` is increasing on `(-oo,oo)` and has neither a local maximum nor a local minimum at `x=0.`

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