SOLUTION: I am having difficulty with this equation. Find the inverse of the function, f(x) = (3 + 2x)/(2-5x)

Algebra ->  Inverses -> SOLUTION: I am having difficulty with this equation. Find the inverse of the function, f(x) = (3 + 2x)/(2-5x)       Log On


   

Question 73977This question is from textbook
: I am having difficulty with this equation.
Find the inverse of the function,
f(x) = (3 + 2x)/(2-5x)
 This question is from textbook

Found 2 solutions by jim_thompson5910, Earlsdon:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Start with given equation
Switch the x and y variables
Now solve for y
Multiply both sides by (2-5y)
Distribute the x on the left side
Get all y terms to one side
Factor out a y
Divide both sides by (2+5x)
Here's our inverse function. In other words


Check:
If we let x=1 and plugged it into we would get


If we plug in in for x into our inverse equation we should get y=1 out.





So this verifies that is our answer. Hope all of this makes sense.


Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
To find the inverse of a function, set the function equal to y , exchange the x's and the y, then solve for y. The given function is: f%28x%29+=+%283%2B2x%29%2F%282-5x%29 Set the function = y'
y+=+%283%2B2x%29%2F%282-5x%29 Exchange the x's for y.
x+=+%283%2B2y%29%2F%282-5y%29 Now solve for y. Multiply both sides by (2-5y)
x%282-5y%29+=+3%2B2y Simplify the left side.
2x-5xy+=+3%2B2y Add 5xy to both sides.
2x+=+3%2B5xy%2B2y Subtract 3 from both sides.
2x-3+=+5xy%2B2y Factor yhe y on the right side.
2x-3+=+y%285x%2B2%29 Divide both sides by (5x+2)
%282x-3%29%2F%285x%2B2%29+=+y, so...
f%5E%28-1%29%28x%29+=+%282x-3%29%2F%285x%2B2%29
Checking ths solution:
We want to show that:
f%28f%5E%28-1%29%28x%29%29+=+x
Simplify the right side.
Continue to simplify.

f%28%282x-3%29%2F%285x%2B2%29%29+=+%2815x%2B6%2B4x-6%29%2F%2810x%2B4-10x%2B15%29=19x%2F19+=+x Whew!!!
So, f%28f%5E%28-1%29%28x%29%29+=+x