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Writing Linear Equations in Standard Form
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The Square of a Binomial
Solving Equations
Adding and Subtracting Like Fractions
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Finding the Equation of an Inverse Function
Slope of a Line
Rules for Nonnegative Integral Exponents

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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 · 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).