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North pre-calculus 1.5 ws key
Chapter 1 Functions and Their Graphs
Section 1.5 Inverse Functions
Section Objectives: Students will know how to find inverses of functions
graphically and algebraically.
I. The Inverse of a Function (pp. 120 - 122)
Relate the concept of inverse functions, with the composition of functions
as the operation, to multiplication and the real numbers. So, if we form the
composition of two functions we should get the identity function h(x) = x.
So to speak, inverse functions “undo” each other. Also note that, if the
function is given as a set of ordered pairs, its inverse would have all the x’s
interchanged with their corresponding y’s.
Ms. Qiu
North pre-calculus 1.5 ws key
Example 2
Match the graph of the function with the graph of its inverse. [The graphs of the inverse functions
are labeled (a), (b), (c), and (d).]
(a)
(b)
(c)
(d)
(I)
(II)
Example 3. Which of the following functions will have an inverse that
is a function.
a)
b)
Example 4: Is the function
Algebraic Solution
one-to-one?
Graphical Solution
Ms. Qiu
North pre-calculus 1.5 ws key
Determine algebraically whether the function is one-to-one. If it is, find its inverse. Verify your
answer graphically.
Example 5a
Algebraic Solution
Graphical Solution
.
Example 5b
Algebraic Solution
Graphical Solution
Ms. Qiu
North pre-calculus 1.5 ws key
III. The Existence of an Inverse Function (p. 124)
Verify the inverse function(algebraically, Numerically, graphically)
Algebraically
Numerically,
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Graphically
North pre-calculus 1.5 ws key
Ms. Qiu
North pre-calculus 1.5 ws key
Verify the inverse function(algebraically, Numerically, graphically)
Algebraically
Ms. Qiu
North pre-calculus 1.5 ws key
Numerically,
Graphically
Example 7 Use the graph of the function f to complete the table and sketch the graph of
(a)
(b)
x
x
-4
-2
2
3
-3
-2
0
6
.