With the given reflection \begin{align} f(7x-5)=2x-1 \end{align} How would I find this reflection, any orientation would be appreciated!
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1What do you propose to start tackling this? – Mark Viola Dec 08 '16 at 22:19
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Give some different but suitable values for x, that's how I was thinking of starting it – user397419 Dec 08 '16 at 22:20
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1Does letting $y=7x-5$ and analyzing with respect to $y$ facilitate? Or how does letting $g(x)=f(7x-5)$ help a bit here? Writing down your ideas and adding them to your post might help you and might induce others to help you further. – Mark Viola Dec 08 '16 at 22:24
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I don't quite understand, I'm really stuck here – user397419 Dec 08 '16 at 22:40
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hint: $ u = 7x-5 \implies f(u) = 2\left(\dfrac{u+5}{7}\right) - 1 = \dfrac{2u+10}{7} - 1= \dfrac{2u+3}{7}\implies f(x) = \dfrac{2x+3}{7}$. To find the inverse, switch $x$ and $y$ in the last equation we have: $x = \dfrac{2y+3}{7} \implies y = \dfrac{7x-3}{2} = f^{-1}(x)$.
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I kept analyzing this but I can't quite get it, I've just started learning functions so a more beginner friendly explanation would be very much appreciated! – user397419 Dec 08 '16 at 22:41
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Yeah, I misinterpreted the actual problem here, this was actually very easy to understand, thanks anyway! – user397419 Dec 08 '16 at 23:45