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Prime Factors
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Working with Percentages and Proportions
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Negative Rational Exponents
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Multiplication Property of Equality
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Product and Quotient of Functions
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Laws of Exponents
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Vertical Line Test
Solving Inequalities with Fractions and Parentheses
Multiplying Polynomials
Solving Quadratic and Polynomial Equations
Extraneous Solutions
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Finding the Equation of an Inverse Function

The following procedure is helpful when trying to find the equation of the inverse of a function.

Procedure — To Find the Equation of the Inverse of a Function

If a function f(x) has an inverse, the following may be used to find the inverse function f -1(x).

Step 1 Replace f(x) with y.

Step 2 Switch the variables y and x.

Step 3 Solve for y.

Step 4 Replace y with f -1(x).



Why do we switch x and y when finding an inverse function?

 This is because if the function f(x) is satisfied by an ordered pair (a, b) then the inverse function f -1(x) is satisfied by the ordered pair (b, a).



Given f(x) = 12x - 7, find f -1(x).


Step 1

Step 2

Step 3

Replace f(x) with y.

Switch the variables y and x.

Solve for y.

Add 7 to both sides.




x + 7

= 12x - 7

= 12y - 7


= 12y

  Divide both sides by 12. = y
  We usually write y on the left. y
Step 4 Replace y with f -1(x). f-1(x)
So, the inverse of f(x) = 12x - 7 is


Notice that in f(x) = 12x - 7, the input is multiplied by 12 and then 7 is subtracted from that product.

The reverse is true for the inverse. That is, in , 7 is added to the input and then that sum is divided by 12.


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