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# Showing that a function can take any real values if x is real. watch

1. Show that ,if x is real , the function 2-x /(x^2-4x+1) can take any real value.

Hello if anyone can help me prove that, i am stuck.
Im getting negative roots but it says x is real....
2. Set y=f(x) rearrange into a quadratic then find the discriminant which will be a function of y which you can then show is always greater than 0.
Set y=f(x) rearrange into a quadratic then find the discriminant which will be a function of y which you can then show is always greater than 0.
Yes i did all that, but my discriminant is turning to negative.
4. (Original post by Bilbao)
Yes i did all that, but my discriminant is turning to negative.
The question is not entirely correct because the discriminant of is therefore there are two points in for which this quadratic is 0 and hence your function is undefined.

Anyway, ignoring those two points, this is rather missing the actual question, because it wants you to show that takes all the values in rather than . To show this, first find any horizontal asymptotes and show that this graph does indeed cross them. Secondly, show that that you have at some point point(s) along it.

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Updated: February 27, 2018
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