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Find a function f(x) such that the parametric curve could be obtained by flipping the graph of f across the line with slope 1 that goes through the origin.

parametric curve with coordinates (t^14, t^7) for t in the interval [−1, 1]

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Flipping across the line $y=x$ interchanges the roles of $x$ and $y$, so the resulting parametric curve has coordinates $(t^7,t^{14})$. I expect you can now find the equation $y=f(x)$ of this curve. Hint: $t^{14}=(t^7)^2$. Be sure to specify the possible values of $x$.

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is it [-1,1}?.. – Maximiliano Dec 1 '12 at 0:17
Yes it is. Since $t$ ranges from $-1$ to $1$, it follows that $x$, that is, $t^7$, also ranges from $-1$ to $1$. – André Nicolas Dec 1 '12 at 0:21
Do we use the fact that is has slope 1 that goes through the origin? – Maximiliano Dec 1 '12 at 0:33
"Flipping" a curve across the line through the origin with slope $1$ (finding the reflection of the curve in that line) interchanges the roles of $x$ and $y$. You can test this by plotting say $(3,1)$ and $(1,3)$: they are symmetrical about the line $y=x$. If you a line $\ell$ other than $y=x$ and flip across $\ell$, that will not interchange the roles of $x$ and $y$. So the fact we were flipping across $y=x$ was crucial. – André Nicolas Dec 1 '12 at 0:40
thank you for your help! – Maximiliano Dec 1 '12 at 0:44

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