SOLUTION: Hi! I cant get the right answer for this problem. Can you help? Find the inverse function of f. f(x)=( x - 7)/(4 x + 8) thanks for your help!

Algebra ->  Functions -> SOLUTION: Hi! I cant get the right answer for this problem. Can you help? Find the inverse function of f. f(x)=( x - 7)/(4 x + 8) thanks for your help!      Log On


   

Question 198369: Hi!
I cant get the right answer for this problem. Can you help?
Find the inverse function of f.
f(x)=( x - 7)/(4 x + 8)
thanks for your help!
Found 2 solutions by jim_thompson5910, arallie:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=%28x-7%29%2F%284x%2B8%29 Start with the given function.


y=%28x-7%29%2F%284x%2B8%29 Replace f(x) with y


x=%28y-7%29%2F%284y%2B8%29 Switch each x with y (and vice versa). The goal now is to solve for y


x%284y%2B8%29=y-7 Multiply both sides by 4y%2B8.


4xy%2B8x=y-7 Distribute


4xy=y-7-8x Subtract 8x from both sides.


4xy-y=-7-8x Subtract y from both sides.


4xy-y=-8x-7 Rearrange the terms.


y%284x-1%29=-8x-7 Factor out the GCF 'y'


y=%28-8x-7%29%2F%284x-1%29 Divide both sides by 4x-1.


So the inverse is

Answer by arallie(162) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=%28x-7%29%2F%284x%2B8%29
f%5E-1%28x%29=?
y=%28x-7%29%2F%284x%2B8%29
Invert
x=%28y-7%29%2F%284y%2B8%29
Solve for y
x%284y%2B8%29=y-7
4xy%2B8x=y-7
4xy-y=-8x-7
y%284x-1%29=-8x-7
y=%28-8x-7%29%2F%284x-1%29
So
If f%28x%29=%28x-7%29%2F%284x%2B8%29
Then f%5E-1%28x%29=%28-8x-7%29%2F%284x-1%29