1. One-to-One Functions;
Section 5.1
Composite Functions
and
Section 5.2
One-to-One Functions;
Inverse Functions
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2. Form a composite function. Find the domain of a composite function.
Objectives
Form a composite function.
Find the domain of a composite function.
Determine whether a function is one-to-one.
Determine the inverse of a function defined by a set of ordered pair.
Obtain the graph of the inverse function from the graph of the function.
Find the inverse of a function defined by an equation.
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5. The domain of g is all real numbers as is the domain of the composite function, so the domain of f ◦ g is the set of all real numbers.
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6. The domain of f is all real numbers as is the domain of the composite function, so the domain of g ◦ f is the set of all real numbers.
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13. For each function, use the graph to determine whether the function is one-to-one.
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14. A function that is increasing on an interval I is a one-to-one function in I.
A function that is decreasing on an interval I is a one-to-one function on I.
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16. State the domain and range of the function and its inverse.
Find the inverse of the following one-to-one function:
{(-5,1),(3,3),(0,0), (2,-4), (7, -8)}
State the domain and range of the function and its inverse.
The inverse is found by interchanging the entries in each ordered pair:
{(1,-5),(3,3),(0,0), (-4,2), (-8,7)}
The domain of the function is {-5, 0, 2, 3, 7}
The range of the function is {-8, -4,0 ,1, 3). This is also the domain of the inverse function.
The range of the inverse function is {-5, 0, 2, 3, 7}
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27. Homework
5.1 #5, 6, 9, 11, 21, 25, 27, 35, 45, 53
5.2 #7, odd, 33, 43, 51, 53, 65, 73, 77
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