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Inverse Functions
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Key Concepts:
Terms in this set (16)
Inverse Function
If a function is named f, this can be written as f⁻¹
One-to-one Function
A property of functions where the same value for y is never paired with two different values of x (the function passes the horizontal line test)
Horizontal Line Test
A way to establish if a function is one-to-one when looking at a function's graph.
Steps to solve algebraically for the inverse of the function
1. Replace f(x) with y in the equation for f(x)
2. Interchange x and y
3. Solve for y.
4. Replace y with f⁻¹(x)
The inverse of f(x) = x + 11
f⁻¹(x) = x - 11
The inverse of f(x) = 2x - 16
f⁻¹(x) = ½x + 8
Vertical Line Test
A way to establish that a relation is a function.
Reflection about the line y = x.
A way to graphically see if two functions are inverses of each other.
Domain
The set of all input values of a relation.
Range
The set of all output values of a relation.
Domain Restriction
Omitting specific values from a relation's set of input values, commonly to ensure that a function's inverse is also a function.
The inverse of f(x) = x³ + 1
f⁻¹(x) = ³√(x-1)
The inverse of f(x) = (x + 1)³
f⁻¹(x) = ³√x - 1
The inverse of f(x) = 2(x - 16)
f⁻¹(x) = ½x + 16
The domain of the inverse of f(x) = x²
[ 0 , ∞ )
The range of the inverse of f(x) = x³
( -∞ , ∞ )
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