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WORKSHEET 7_4 Inverse Functions.pdf

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WORKSHEET 7.4 INVERSE FUNCTIONS
Inverse Relations
Find the inverse for each relation.
1.
{ (1, -3), (-2, 3), (5, 1), (6, 4) }
2.
{ (-5, 7), (-6, -8), (1, -2), (10, 3) }
Finding Inverses
Find an equation for the inverse for each of the following relations.
3.
y пЂЅ 3x пЂ« 2
4.
y пЂЅ пЂ­5x пЂ­ 7
5.
y пЂЅ 12x пЂ­ 3
6.
y пЂЅ пЂ­8x пЂ« 16
7.
yпЂЅ
2
xпЂ­5
3
8.
yпЂЅпЂ­
9.
yпЂЅпЂ­
10.
yпЂЅ
1
xпЂ«8
2
11.
y пЂЅ x2 пЂ« 5
12.
y пЂЅ x2 пЂ­ 4
13.
y пЂЅ ( x пЂ« 3)2
14.
y пЂЅ ( x пЂ­ 6)2
15.
y пЂЅ x пЂ­ 2, y п‚і 0
16.
y пЂЅ x пЂ« 5, y п‚і 0
17.
y пЂЅ x пЂ« 8, y п‚і 8
18.
y пЂЅ x пЂ­ 7, y п‚і пЂ­7
5
x пЂ« 10
8
3
xпЂ«5
4
Verifying Inverses
Verify that f and g are inverse functions.
20.
f ( x ) пЂЅ 5x пЂ« 2, g( x ) пЂЅ
xпЂ­2
5
1
x пЂ­3
3
22.
f ( x ) пЂЅ 2x пЂ­ 7, g( x ) пЂЅ
xпЂ«7
2
1
xпЂ«2
4
24.
f ( x) пЂЅ
19.
f ( x) пЂЅ x пЂ« 6, g( x) пЂЅ x пЂ­ 6
21.
f ( x ) пЂЅ пЂ­3 x пЂ­ 9, g ( x ) пЂЅ пЂ­
23.
f ( x ) пЂЅ пЂ­4x пЂ« 8, g( x ) пЂЅ пЂ­
1
x пЂ­ 7, g( x ) пЂЅ 2x пЂ« 14
2
continued on back
Graphing Inverses
Graph the inverse for each relation below (put your answer on the same graph).
25.
26.
27.
28.
ANSWERS – Worksheet 7.4
1.
{ (-3, 1), (3, -2), (1, 5), (4, 6) }
2.
{ (7, -5), (-8, -6), (-2, 1), (3, 10) }
3.
yпЂЅ
4.
y пЂЅпЂ­
5.
yпЂЅ
xпЂ«3
12
6.
yпЂЅ
1
xпЂ­2
8
7.
yпЂЅ
3
15
xпЂ«
2
2
8.
yпЂЅпЂ­
9.
y пЂЅпЂ­
10.
y пЂЅ 2x пЂ­ 16
11.
yпЂЅп‚± xпЂ­5
12.
yпЂЅп‚± xпЂ«4
13.
y пЂЅ пЂ­3 п‚± x
14.
yпЂЅ6п‚± x
15.
y пЂЅ x2 пЂ« 2, x п‚і 0
16.
y пЂЅ x2 пЂ­ 5, x п‚і 0
17.
y пЂЅ ( x пЂ­ 8)2, x п‚і 8
18.
y пЂЅ ( x пЂ« 7)2, x п‚і пЂ­7
19.
verify
20.
verify
21.
verify
22.
verify
23.
verify
24.
verify
25.
xпЂ­2
3
xпЂ«7
5
26.
4
20
xпЂ«
3
3
8
x пЂ­ 16
5
27.
28.
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