1. ## Inverse functions

find a formula for the inverse of the function:

f(x) = (4x-1)/(2x+3)

i substituted f(x) for x and tried solving, and i ended up with (3x+1)/2, but that doesnt check

any help would be appreciated..

2. Swap out your x and y

$\displaystyle x=\frac{4y-1}{2y+3}$

Now, divide so you can solve for y easier:

$\displaystyle \frac{4y-1}{2y+3}=2-\frac{7}{2y+3}$

Now, continue?.

3. Originally Posted by skabani
find a formula for the inverse of the function:

f(x) = (4x-1)/(2x+3)

i substituted f(x) for x and tried solving, and i ended up with (3x+1)/2, but that doesnt check

any help would be appreciated..
so you want to solve $\displaystyle x = \frac {4y - 1}{2y + 3}$ for $\displaystyle y$

$\displaystyle \Rightarrow x(2y + 3) = 4y - 1$ .........multiplied both sides by $\displaystyle 2y + 3$

$\displaystyle \Rightarrow 2xy + 3x = 4y - 1$ ..........expanded the brackets on the left

$\displaystyle \Rightarrow 4y - 2xy = 3x + 1$ ..........added $\displaystyle 1 - 2xy$ on both sides

$\displaystyle \Rightarrow y(4 - 2x) = 3x + 1$ .........factored out $\displaystyle y$ from the left hand side

$\displaystyle \Rightarrow y = \frac {3x + 1}{4 - 2x}$