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 September 2nd, 2014, 09:45 AM #1 Senior Member   Joined: Nov 2013 Posts: 434 Thanks: 8 range of y Find range of y=(1-x^2)/(1+x^2) Last edited by skipjack; September 2nd, 2014 at 11:47 AM. September 2nd, 2014, 10:16 AM #2 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,675 Thanks: 2655 Math Focus: Mainly analysis and algebra $$\lim_{x \to -\infty} y = \lim_{x \to +\infty} y = -1 \\ \frac{\mathbb{d}y}{\mathbb{d}x} = 0 \implies x=0 \\ y(0) = 1$$ and $y$ is bounded everywhere. So the range of $y$ is $(-1, 1]$. September 2nd, 2014, 11:59 AM #3 Global Moderator   Joined: Dec 2006 Posts: 20,942 Thanks: 2210 As y = -1 + 2/(1 + x²) = 1 - 2x²/(1 + x²), y ∈ (-1,1]. Tags rang, range Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode

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