Find a range of $frac4x - 12x + 3$Finding the range of rational functionsFind a rational function $f: mathbb R rightarrow mathbb R$ with range $f(mathbb R)=[-1,1]$Finding a Rational FunctionWhat is the possible domain and range for this rational function?Domain and Range of a rational functionA question about the domain of definition of rational functionsRange of a Rational FunctionFinding the domain of a three variable functionHow to find range of a rational function without using derivativesRange of a Rational Function with arbitrary constant
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Find a range of $frac4x - 12x + 3$
Finding the range of rational functionsFind a rational function $f: mathbb R rightarrow mathbb R$ with range $f(mathbb R)=[-1,1]$Finding a Rational FunctionWhat is the possible domain and range for this rational function?Domain and Range of a rational functionA question about the domain of definition of rational functionsRange of a Rational FunctionFinding the domain of a three variable functionHow to find range of a rational function without using derivativesRange of a Rational Function with arbitrary constant
$begingroup$
Given a function $frac4x - 12x + 3$
I know its Domain is $x in mathbbR $
But how can I find its range?
Any hint is appreciated.
rational-functions
asked Mar 21 at 6:16
OOD WaterballOOD Waterball
1325
$endgroup$
add a comment |
$begingroup$
Given a function $frac4x - 12x + 3$
I know its Domain is $x in mathbbR $
But how can I find its range?
Any hint is appreciated.
rational-functions
asked Mar 21 at 6:16
OOD WaterballOOD Waterball
1325
$endgroup$
add a comment |
$begingroup$
Given a function $frac4x - 12x + 3$
I know its Domain is $x in mathbbR $
But how can I find its range?
Any hint is appreciated.
rational-functions
asked Mar 21 at 6:16
OOD WaterballOOD Waterball
1325
$endgroup$
Given a function $frac4x - 12x + 3$
I know its Domain is $x in mathbbR $
But how can I find its range?
Any hint is appreciated.
rational-functions
rational-functions
asked Mar 21 at 6:16
OOD WaterballOOD Waterball
1325
asked Mar 21 at 6:16
OOD WaterballOOD Waterball
1325
asked Mar 21 at 6:16
OOD WaterballOOD Waterball
1325
asked Mar 21 at 6:16
OOD WaterballOOD Waterball
1325
asked Mar 21 at 6:16
OOD WaterballOOD Waterball
1325
1325
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Write $y = frac4x-12x-3$, and make $x$ the subject of the equation :
$$
y = frac4x-12x-3 implies 2xy-3y = 4x- 1 implies 2xy-4x = 3y-1 overset?implies x = frac3y-12y-4
$$
which tells you that for any $y$ such that $frac3y-12y-4$ is in the domain(and such that the last transformation makes sense), we have $fleft(frac3y-12y-4right) = y$. So any such $y$ is in the range, in fact the range is made up of all such $y$. Now, can you find the range of the function?
answered Mar 21 at 6:19
астон вілла олоф мэллбэргастон вілла олоф мэллбэрг
40.2k33577
$endgroup$
$begingroup$
Thanks for your helpful explanation, now I got some directions to do the similar cases.
$endgroup$
– OOD Waterball
Mar 21 at 6:25
1
$begingroup$
You are welcome! Also note that you can close the question if you are satisfied : you can refer to it later if you are having similar questions.
$endgroup$
– астон вілла олоф мэллбэрг
Mar 21 at 6:26
add a comment |
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1 Answer
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1 Answer
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$begingroup$
Write $y = frac4x-12x-3$, and make $x$ the subject of the equation :
$$
y = frac4x-12x-3 implies 2xy-3y = 4x- 1 implies 2xy-4x = 3y-1 overset?implies x = frac3y-12y-4
$$
which tells you that for any $y$ such that $frac3y-12y-4$ is in the domain(and such that the last transformation makes sense), we have $fleft(frac3y-12y-4right) = y$. So any such $y$ is in the range, in fact the range is made up of all such $y$. Now, can you find the range of the function?
answered Mar 21 at 6:19
астон вілла олоф мэллбэргастон вілла олоф мэллбэрг
40.2k33577
$endgroup$
$begingroup$
Thanks for your helpful explanation, now I got some directions to do the similar cases.
$endgroup$
– OOD Waterball
Mar 21 at 6:25
1
$begingroup$
You are welcome! Also note that you can close the question if you are satisfied : you can refer to it later if you are having similar questions.
$endgroup$
– астон вілла олоф мэллбэрг
Mar 21 at 6:26
add a comment |
$begingroup$
Write $y = frac4x-12x-3$, and make $x$ the subject of the equation :
$$
y = frac4x-12x-3 implies 2xy-3y = 4x- 1 implies 2xy-4x = 3y-1 overset?implies x = frac3y-12y-4
$$
which tells you that for any $y$ such that $frac3y-12y-4$ is in the domain(and such that the last transformation makes sense), we have $fleft(frac3y-12y-4right) = y$. So any such $y$ is in the range, in fact the range is made up of all such $y$. Now, can you find the range of the function?
answered Mar 21 at 6:19
астон вілла олоф мэллбэргастон вілла олоф мэллбэрг
40.2k33577
$endgroup$
$begingroup$
Thanks for your helpful explanation, now I got some directions to do the similar cases.
$endgroup$
– OOD Waterball
Mar 21 at 6:25
1
$begingroup$
You are welcome! Also note that you can close the question if you are satisfied : you can refer to it later if you are having similar questions.
$endgroup$
– астон вілла олоф мэллбэрг
Mar 21 at 6:26
add a comment |
$begingroup$
Write $y = frac4x-12x-3$, and make $x$ the subject of the equation :
$$
y = frac4x-12x-3 implies 2xy-3y = 4x- 1 implies 2xy-4x = 3y-1 overset?implies x = frac3y-12y-4
$$
which tells you that for any $y$ such that $frac3y-12y-4$ is in the domain(and such that the last transformation makes sense), we have $fleft(frac3y-12y-4right) = y$. So any such $y$ is in the range, in fact the range is made up of all such $y$. Now, can you find the range of the function?
answered Mar 21 at 6:19
астон вілла олоф мэллбэргастон вілла олоф мэллбэрг
40.2k33577
$endgroup$
Write $y = frac4x-12x-3$, and make $x$ the subject of the equation :
$$
y = frac4x-12x-3 implies 2xy-3y = 4x- 1 implies 2xy-4x = 3y-1 overset?implies x = frac3y-12y-4
$$
which tells you that for any $y$ such that $frac3y-12y-4$ is in the domain(and such that the last transformation makes sense), we have $fleft(frac3y-12y-4right) = y$. So any such $y$ is in the range, in fact the range is made up of all such $y$. Now, can you find the range of the function?
answered Mar 21 at 6:19
астон вілла олоф мэллбэргастон вілла олоф мэллбэрг
40.2k33577
answered Mar 21 at 6:19
астон вілла олоф мэллбэргастон вілла олоф мэллбэрг
40.2k33577
answered Mar 21 at 6:19
астон вілла олоф мэллбэргастон вілла олоф мэллбэрг
40.2k33577
answered Mar 21 at 6:19
астон вілла олоф мэллбэргастон вілла олоф мэллбэрг
40.2k33577
40.2k33577
$begingroup$
Thanks for your helpful explanation, now I got some directions to do the similar cases.
$endgroup$
– OOD Waterball
Mar 21 at 6:25
1
$begingroup$
You are welcome! Also note that you can close the question if you are satisfied : you can refer to it later if you are having similar questions.
$endgroup$
– астон вілла олоф мэллбэрг
Mar 21 at 6:26
add a comment |
$begingroup$
Thanks for your helpful explanation, now I got some directions to do the similar cases.
$endgroup$
– OOD Waterball
Mar 21 at 6:25
1
$begingroup$
You are welcome! Also note that you can close the question if you are satisfied : you can refer to it later if you are having similar questions.
$endgroup$
– астон вілла олоф мэллбэрг
Mar 21 at 6:26
$begingroup$
Thanks for your helpful explanation, now I got some directions to do the similar cases.
$endgroup$
– OOD Waterball
Mar 21 at 6:25
$begingroup$
Thanks for your helpful explanation, now I got some directions to do the similar cases.
$endgroup$
– OOD Waterball
Mar 21 at 6:25
1
1
$begingroup$
You are welcome! Also note that you can close the question if you are satisfied : you can refer to it later if you are having similar questions.
$endgroup$
– астон вілла олоф мэллбэрг
Mar 21 at 6:26
$begingroup$
You are welcome! Also note that you can close the question if you are satisfied : you can refer to it later if you are having similar questions.
$endgroup$
– астон вілла олоф мэллбэрг
Mar 21 at 6:26
add a comment |
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