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Level 211

Using Inverse Operations


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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