9.2.2 Functions and Their Inverses − Practice (continued)
2. Use the horizontal line test to identify the relation whose inverse is not a function. ○ ○
y
y
5 4 3 2 1
5 4 3 2 1
2 3 4 5 x
2 3 4 5 x
–5 –4 –3 –2
– –1 1 –2 –3 –4 –5
1
–5 –4 –3 –2
– –1 1 –2 –3 –4 –5
1
○
○
y
y
5 4 3 2 1
5 4 3 2 1
2 3 4 5 x
2 3 4 5 x
–5 –4 –3 –2
– –1 1 –2 –3 –4 –5
1
–5 –4 –3 –2
– –1 1 –2 –3 –4 –5
1
4. Find the inverse of f ( x ) = x 3 − 3. Determine whether it is a function and state its domain and range.
3. Find the inverse of f ( x ) = x 2 − 4. Determine whether it is a function and state its domain and range.
6. Use composition to identify the functions that are inverses of each other. ○ f x x g x x ( ) 3 2 5 ; ( ) 5 2 3 = + = + ○ f x x g x x ( ) 8; ( ) 10 = − = +
5. Find the inverse of the function. f x x ( ) 2 3 4 = −
4 5
5 4
2
x
3
+
○ f x
x g x 2 6; ( )
( )
= +
=
2
3
x
3
○ f x
g x 3; ( )
x 8 3
( )
= −
= +
8
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