Finding the Equation of an Inverse Function
Example
Given
,
find f^{1}(x).
Solution
Step 1 
Replace f(x) with y.

y 

Step 2 
Switch the variables y and x.

x 

Step 3 
Solve for y. 



Multiply each side by the LCD, 2y. 
2y Â· x 


Simplify. Add 20y to both sides.
Factor out y. 
2xy 2xy + 20y
y(2x + 20) 
= 7  20y = 7
= 7 

Divide both sides by 2x + 20. 
y 

Step 4 
Replace y with f^{ 1}(x). 
f^{1}(x) 

So, the inverse of
is f^{1}(x)
Note:
Here is another way to solve
for y:
Add 10 to both sides. 

Multiply by the LCD, 2y. 

Simplify on the right. 
2y(x + 10) = 7 
Divide both sides by 2(x + 10). 

