7.7 Inverse Relations and Functions

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7.7 Inverse Relations and Functions
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Using a graphing calculator, graph the pairs of
equations on the same graph. Sketch your results.
Be sure to use the negative sign, not the
subtraction key.
These graphs are said to be inverses of each
other.
What do you notice about the graphs?
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An inverse relation undoes the relation and
switches the x and y coordinates.

• In other words, if the relation has coordinates
  (a, b), the inverse has coordinates of (b,a)

Function f(x)
Inverse of Function f(x)
X Y
0 3
1 4
-3 0
-5 2
2 5
-8 5
X Y
3 0
4 1
0 -3
2 -5
5 2
5 -8
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Lets look at our graphs from earlier. Notice
that the points of the graphs are reflected
across a specific line.
What is the equation of the line of reflection?
y x
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Finding the Inverse of an equation
Find the inverse of yx23 xy23 x 3 y2
Switch the x and y Solve for y Find the square
root of both sides
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What happens if I dont include the ?

• Graphing the function and only the positive graph
  of the inverse . . .

We only get half of the inverse graph.
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Finding the Inverse of a function
When we find the inverse of a function f(x) we
write it as f-1
Find the inverse of
Rewrite using y Switch the x and y Square both
sides Solve for y
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Lets Try Some
Find the inverse of each
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Lets Try Some
Find the inverse of each
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Composition of Inverse Functions
For the function