Operations on Functions

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Operations on Functions
Composite Function
Combining a function within another function.
Written as follows
Operations Notation
Sum
Difference
Product
Quotient
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Example 1 Add / Subtract Functions
a)
b)
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Example 2 Multiply / Divide Functions
a)
b)
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Example 3 Evaluate Composites of Functions
Recall (a b)2 a2 2ab b2
a)
b)
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Example 4 Composites of a Function Set
a)
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Example 4 Composites of a Function Set
b)
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Inverse Functions and Relations
Inverse Relation
Relation (function) where you switch the Domain
and range values
Inverse Notation
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Steps to Find Inverses
1 Replace f(x) with y
2 Interchange x and y
One-to-One
A function whose inverse is also a function
(horizontal line test)
Inverse is not a function
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Example 1 Inverses of Ordered Pair Relations
a)
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Inverses of Graphed Relations

• The graphs of inverses are reflections about the
  line yx

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Example 2 Find an Inverse Function
a)
b)
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Example 2 Continued
c)
d)
Inverse is not a 1-1 function. (BUT the inverse
is 2 different functions If you restrict the
domain in the original function, then the inverse
will become a function.
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Example 3 Verify two Functions are Inverses
a) Method 1
b) Method 2
Yes, Inverses
Yes, Inverses
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Example 4 One-to-One (Horizontal Line Test)
Determine whether the functions are one-to-one.
a)
b)
One-to-One
Not One-to-One