Im trying to find the inverse of the function with working, see attached image

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- Nov 28th 2009, 04:08 AMhunterage2000inverse of a function
Im trying to find the inverse of the function with working, see attached image

- Nov 28th 2009, 04:17 AMBacterius
$\displaystyle f(x) = \frac{2 - 3x}{4x + 5}$

Say $\displaystyle f(x) = y$

$\displaystyle y = \frac{2 - 3x}{4x + 5}$

Thus :

$\displaystyle y(4x + 5) = 2 - 3x$

Expand :

$\displaystyle 4xy + 5y = 2 - 3x$

Rearrange terms :

$\displaystyle 4xy + 3x = 2 - 5y$

Factorize $\displaystyle x$ :

$\displaystyle x(4y + 3) = 2 - 5y$

Make x the subject by dividing :

$\displaystyle x = \frac{2 - 5y}{4y + 3}$

Thus the inverse function of $\displaystyle f(x)$ is $\displaystyle f(x)^{-1} = \frac{2 - 5x}{4x + 3}$

Does it make sense ? - Nov 28th 2009, 04:27 AMhunterage2000
Cheers Ray that is spot on (Rock)

- Nov 28th 2009, 04:29 AMRaoh
put $\displaystyle y=\frac{2-3x}{4x+5}$,flip $\displaystyle x$ and $\displaystyle y$ ,$\displaystyle x=\frac{2-3y}{4y+5}$ and solve for $\displaystyle y$.

$\displaystyle x=\frac{2-3y}{4y+5}\Leftrightarrow x\left ( 4y+5 \right )$=$\displaystyle 2-3y\Leftrightarrow 4xy+3y+5x$=$\displaystyle 2\Leftrightarrow y\left ( 4x+3 \right )$=$\displaystyle 2-5x\Leftrightarrow y=\frac{2-5x}{4x+3}$

and hence the inverse is $\displaystyle f^{-1}(x)=\frac{2-5x}{4x+3}$ - Nov 28th 2009, 04:30 AMBacterius
By the way, this trick can help you find answers easily so as to be able to solve this type of questions quicker : can you spot some kind of relation between the numbers in the function and the numbers in the inverse function ? (Nod)

EDIT : woah Raoh now this is "compressed" maths, now I realize how much of a waste of paper my writing style would be in an exam (Doh). I detailed carefully each step because Hunterage asked for it though (Sweating). - Nov 28th 2009, 06:33 AMe^(i*pi)