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I am completely confused as to how to answer this. I can answer other questions in this topic but this one is confusing me. Help please?

What are the elements in the set: $S_b=\{(x,y):(x,y) \in \mathbb R^2 \textrm{ and } y=x/4 \textrm{ and } y=4/x\}$

I have found that $x=4$ and $x=-4$, which means that $y=-1$ or $y=1$
Are these the elements ?

amrsa
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MathGeek101
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    This implies that $\frac{4}{x} = \frac{x} {4}$ which you can solve. – Student Mar 06 '19 at 21:14
  • Hi, welcome! What have you tried so far? Did you maybe try to combine both restrictions, $y=x/4$ and $y=4/x$? – Stan Tendijck Mar 06 '19 at 21:15
  • To be precise, the two solutions are $(4, 1)$ and $(-4, -1)$. Your answer is correct. Do you see why those are the only answers? (Check out the first comment above.) – Robert Shore Mar 06 '19 at 21:29
  • Is it because you can only use real numbers? – MathGeek101 Mar 06 '19 at 21:34
  • Actually, no. You'd have the same solutions if you allowed complex numbers. Do you understand the implication of the first comment above? – Robert Shore Mar 06 '19 at 22:04
  • Yeah. As they both equal y they also equal each other so you can then solve for x and ultimately solve for y by placing the value of x back into the original equation. – MathGeek101 Mar 06 '19 at 22:15

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