How do i show that this function :$f(x)=alpha x +beta+ frac{gamma}{alpha'+beta' x}$ always have symetric...
$begingroup$
let $f$ be a real valued function defined as $f(x)=alpha x +beta+ frac{gamma}{alpha'+beta' x}$ , I want a simple method to show that every function of the precedent form always has a symetric center point ?
I have tried to show that using this basic : $f(2alpha-x)=2beta-f(x)$ but i didn't succeed , However this basic always work , And always the symetric point in this case is $M( -frac{alpha'}{beta'}, f( -frac{alpha'}{beta'}))$
real-analysis even-and-odd-functions
asked Jan 12 at 15:43
zeraoulia rafikzeraoulia rafik
2,39711134
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add a comment |
$begingroup$
let $f$ be a real valued function defined as $f(x)=alpha x +beta+ frac{gamma}{alpha'+beta' x}$ , I want a simple method to show that every function of the precedent form always has a symetric center point ?
I have tried to show that using this basic : $f(2alpha-x)=2beta-f(x)$ but i didn't succeed , However this basic always work , And always the symetric point in this case is $M( -frac{alpha'}{beta'}, f( -frac{alpha'}{beta'}))$
real-analysis even-and-odd-functions
asked Jan 12 at 15:43
zeraoulia rafikzeraoulia rafik
2,39711134
$endgroup$
$begingroup$
It's a lot easier to enter if you write $f(x)=a+bx+c/(d+ex)$.
$endgroup$
– marty cohen
Jan 12 at 16:16
add a comment |
$begingroup$
let $f$ be a real valued function defined as $f(x)=alpha x +beta+ frac{gamma}{alpha'+beta' x}$ , I want a simple method to show that every function of the precedent form always has a symetric center point ?
I have tried to show that using this basic : $f(2alpha-x)=2beta-f(x)$ but i didn't succeed , However this basic always work , And always the symetric point in this case is $M( -frac{alpha'}{beta'}, f( -frac{alpha'}{beta'}))$
real-analysis even-and-odd-functions
asked Jan 12 at 15:43
zeraoulia rafikzeraoulia rafik
2,39711134
$endgroup$
let $f$ be a real valued function defined as $f(x)=alpha x +beta+ frac{gamma}{alpha'+beta' x}$ , I want a simple method to show that every function of the precedent form always has a symetric center point ?
I have tried to show that using this basic : $f(2alpha-x)=2beta-f(x)$ but i didn't succeed , However this basic always work , And always the symetric point in this case is $M( -frac{alpha'}{beta'}, f( -frac{alpha'}{beta'}))$
real-analysis even-and-odd-functions
real-analysis even-and-odd-functions
asked Jan 12 at 15:43
zeraoulia rafikzeraoulia rafik
2,39711134
asked Jan 12 at 15:43
zeraoulia rafikzeraoulia rafik
2,39711134
asked Jan 12 at 15:43
zeraoulia rafikzeraoulia rafik
2,39711134
asked Jan 12 at 15:43
zeraoulia rafikzeraoulia rafik
2,39711134
asked Jan 12 at 15:43
zeraoulia rafikzeraoulia rafik
2,39711134
2,39711134
$begingroup$
It's a lot easier to enter if you write $f(x)=a+bx+c/(d+ex)$.
$endgroup$
– marty cohen
Jan 12 at 16:16
add a comment |
$begingroup$
It's a lot easier to enter if you write $f(x)=a+bx+c/(d+ex)$.
$endgroup$
– marty cohen
Jan 12 at 16:16
$begingroup$
It's a lot easier to enter if you write $f(x)=a+bx+c/(d+ex)$.
$endgroup$
– marty cohen
Jan 12 at 16:16
$begingroup$
It's a lot easier to enter if you write $f(x)=a+bx+c/(d+ex)$.
$endgroup$
– marty cohen
Jan 12 at 16:16
add a comment |
1 Answer
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It suffices to note $fleft(x-frac{alpha^{prime}}{beta^{prime}}right)=alpha x+frac{gamma}{beta^{prime}x}+beta-frac{alphaalpha^{prime}}{beta^{prime}}$ is an odd function plus a constant.
answered Jan 12 at 16:21
J.G.J.G.
33.5k23252
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add a comment |
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1 Answer
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$begingroup$
It suffices to note $fleft(x-frac{alpha^{prime}}{beta^{prime}}right)=alpha x+frac{gamma}{beta^{prime}x}+beta-frac{alphaalpha^{prime}}{beta^{prime}}$ is an odd function plus a constant.
answered Jan 12 at 16:21
J.G.J.G.
33.5k23252
$endgroup$
add a comment |
$begingroup$
It suffices to note $fleft(x-frac{alpha^{prime}}{beta^{prime}}right)=alpha x+frac{gamma}{beta^{prime}x}+beta-frac{alphaalpha^{prime}}{beta^{prime}}$ is an odd function plus a constant.
answered Jan 12 at 16:21
J.G.J.G.
33.5k23252
$endgroup$
add a comment |
$begingroup$
It suffices to note $fleft(x-frac{alpha^{prime}}{beta^{prime}}right)=alpha x+frac{gamma}{beta^{prime}x}+beta-frac{alphaalpha^{prime}}{beta^{prime}}$ is an odd function plus a constant.
answered Jan 12 at 16:21
J.G.J.G.
33.5k23252
$endgroup$
It suffices to note $fleft(x-frac{alpha^{prime}}{beta^{prime}}right)=alpha x+frac{gamma}{beta^{prime}x}+beta-frac{alphaalpha^{prime}}{beta^{prime}}$ is an odd function plus a constant.
answered Jan 12 at 16:21
J.G.J.G.
33.5k23252
answered Jan 12 at 16:21
J.G.J.G.
33.5k23252
answered Jan 12 at 16:21
J.G.J.G.
33.5k23252
answered Jan 12 at 16:21
J.G.J.G.
33.5k23252
33.5k23252
add a comment |
add a comment |
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$begingroup$
It's a lot easier to enter if you write $f(x)=a+bx+c/(d+ex)$.
$endgroup$
– marty cohen
Jan 12 at 16:16