geerky42
  • geerky42
I need a quick favor: I want strictly increasing elementary function \(f(x)\) such that \(f(0)=0\), \(f\left(\frac12\right)=1\), and \(\displaystyle \lim_{x\to1^-}f(x) = \infty\). I just want one example of function that satisfies given conditions. Cannot figure this out...
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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Loser66
  • Loser66
How about this \(f(x) =\dfrac{x-x^2}{1-x}\) f(0) =0 \(f(1/2) =\dfrac{1/2-1/4}{1-1/2}=1\) as x approach 1 from the left , lim --> infinitive Does it work?
Loser66
  • Loser66
and if we simplify, we get f(x) =x, it is increasing, right?
ybarrap
  • ybarrap
You think this works? $$ f(x)=\frac{x(x+\frac{3}{2})}{x-1}\\ $$

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ybarrap
  • ybarrap
http://www.wolframalpha.com/input/?i=x%28x%2B3%2F2%29%2F%28x-1%29
Loser66
  • Loser66
@ybarrap but your graph is decreasing from x =-1
ybarrap
  • ybarrap
Or maybe... $$ f(x)=\frac{x(x+\frac{3}{2})}{1-x}\\ $$ http://www.wolframalpha.com/input/?i=x%28x%2B3%2F2%29%2F%281-x%29
geerky42
  • geerky42
@ybarrap Not exactly what I needed, but I modified it to \(f(x) = -\dfrac{x(x+\frac32)}{2(x-1)}\), which works for me. Thanks!
ybarrap
  • ybarrap
Yep, that's it!
geerky42
  • geerky42
@Loser66 Well, I want \(\lim_{x\to1^-}f(x)\) to be \(\infty\),
geerky42
  • geerky42
But I got what I needed, thanks!
Loser66
  • Loser66
ok

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