The Inverse Of A Quadratic Functions Worksheet Page 2
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8How is any quadratic function related to its inverse
K.
a) in their domains and ranges?
b) in their equations?
APPLY the Math
1
Determining the domain and range of the inverse of a quadratic function
EXAMPLE
2
y
Given the graph of
f (x) 5 x
,
2
a) graph the inverse relation
f(x) = x
8
2
b) state the domain and range of
f (x) 5 x
and the inverse relation
6
2
c) determine whether the inverse of
f (x) 5 x
is also a function. Give
4
a reason for your answer.
2
x
0
6
4
2
2
4
6
2
Paul’s Solution
y
a)
2
To graph the inverse of
f(x) 5 x
,
I took the coordinates
2
f(x) = x
of each point on the original graph and switched the
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x- and y-coordinates. For example, (2, 4) became (4, 2).
y = x
6
I had to do this because the input value becomes the
output value in the inverse, and vice versa.
4
The graph of the inverse is a reflection of the original
2
x
function about the line
y 5 x.
0
2
2
4
6
8
2
f -
: + - x
1
4
6
5x [ R6.
2
b) The domain of
f (x) 5 x
is
The range
5 y [ R | y $ 06.
The domain of the inverse is the range of the original
2
of
f (x) 5 x
is
Therefore, the
5x [ R | x $ 06,
function. The range of the inverse is the domain of the
21
domain of
f
is
and the range
original function.
5 y [ R6.
is
2
I knew this because the inverse fails the vertical-line test:
c) The inverse of
f (x) 5 x
is not a function.
For each number in the domain except 0, there are two
values in the range.
156
3.3 The Inverse of a Quadratic Function
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