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Inverse Relations

interchanges the input and output values of the original relation. This means the original domain and range are also interchanged.

The graph of an inverse relation is

a reflection of the original relation across the line y=x

Inverse Functions

when both the relation are inverse relation are functions

f⁻₁(x)

Inverse Function of f(x) is written as

Horizontal Line Test

inverse of a function is also a function if and only if no horizontal line intersects more than one

y=2x-7

Finding Inverse Relations: Ex. 1

y+x²-5

Finding Inverse Relations: Ex. 2

NOT A NEGATIVE EXPONENT

Inverse Functions are written as f⁻₁(x) it is not--

F INVERSE

f⁻₁(x) is read as

VERTICAL LINE TEST

A line is a function is it passes the

h(x)= 20-x/4

x= 20-y/4

f(x)= -2x³ + 3

x= -2y³ + 3

g(x)=1/3x + 8/3

f(x)= 3(1/3x + 8/3)-8 g(x)= 1/3(3x-8) + 8/3

g(x)=1/3x-5/3

f(x)=3(1/3x - 5/3) -5

f(x)= (x-2)²

x= (y-2)²

Equation

A mathematical sentence that contains an equals sign

Variable

an alphabetic character representing a number, called the value, which is either arbitrary or not fully specified or unknown. It is usually a letter like x or y.

equivalent

Equal to

inverse operation

Operations that undo each other

Subtraction

to take a quantity away from another

Addition

to join two or more quantities

Division

process of breaking a quantity into equal parts

Multiplication

process of repeated addition

inequality

A mathematical sentence that shows the relationship between quantities that are not equivalent

<

Less than

>

Greater than

≤

Less than or equal to

≥

Greater than or equal to

≠

Not equal to