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 Depdendent Variable

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 Dependent Variable

 Number of inequalities to solve: 23456789
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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 Â· x Simplify.Add 20y to both sides. Factor out y. 2xy2xy + 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). 