Im trying to find the inverse of the function with working, see attached image
$\displaystyle f(x) = \frac{2 - 3x}{4x + 5}$
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 ?
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 $\displaystyle f^{-1}(x)=\frac{2-5x}{4x+3}$
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 ?
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 . I detailed carefully each step because Hunterage asked for it though .