How do you find the range of #f(x)=(2x^2 -1) / ( x^2 +1)#?

1 Answer
MeneerNask
Jul 23, 2015

You first look for restriction in the domain. In this there are none, since the denominator will always be at least #1#

Explanation:

The minimum value this function can reach is when
#x=0->f(x)=(-1)/1=-1#
The maximum is when #x# gets really large, the function will be nearing #(2x^2)/x^2=2# without reaching it: #lim_(x->oo) f(x)=2#
So the range is #-1<=f(x)<2#
graph{(2x^2-1)/(x^2+1) [-10, 10, -5, 5]}

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