MCR3U1
U3L3
THE INVERSE of a QUADRATIC FUNCTION
PART A ~ INTRODUCTION
Recall the following concepts of an inverse function:
Algebraically: the inverse function is found by interchanging x and y
Graphically: the inverse is a reflection of the original function in the line y = x
Notation:
𝑓 −1 (𝑥) is used to represent the inverse if it is a function
PART B ~ THE INVERSE OF A QUADRATIC FUNCTION
Graph the function, 𝑓(𝑥) = 𝑥 2 , and its inverse. State the domain and range for each.
y
𝑦 = 𝑥2
D=
x
R=
____________________
D=
R=
NOTE:
 the right side of the original parabola
becomes the upper half of the inverse
 the left side of the original parabola
becomes the lower half of the inverse
Is the inverse of 𝑓(𝑥) = 𝑥 2 also a function? How can this be changed?
y
y
x
x
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U3L3
PART C ~ RESTRICTING THE DOMAIN (ORIGINAL OR INVERSE FUNCTION)
The inverse equation may be determined using:
Example 
i) the interchange method
ii) the tally chart short–cut
Determine the inverse of the function, 𝑓(𝑥) = 𝑥 2 + 3. Restrict the domain
for 𝑓(𝑥) so that 𝑓 −1 (𝑥) is a function.
𝑓(𝑥)
y
𝑓 −1 (𝑥)
x
Example 
Determine the inverse of the function, 𝑓(𝑥) = 2(𝑥 − 3)2 − 5, for x  3.
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(the tally chart method may also be used)
𝑓 −1 (𝑥)
𝑓(𝑥)
Example 
Given the graph of a function, 𝑔(𝑥), determine the equation for 𝑔−1 (𝑥).
State the domain and range for each.
 𝑔(𝑥) =
 𝑔−1 (𝑥) =
D=
D=
R=
R=
HOMEWORK: p.160–162 #1–3, 5–7, 10, 13, 14