Download 6.1-6.3 Function Operations-Inverse-Sqrt Review W.S.

6.1-6.3 Review
Name___________________________________
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Function Operations/Inverses/Square Root Functions
Find the inverse of each function.
1
1) h( x) = x - 1
4
h
-1
3
2) f ( x) = -2 + x
2
( x) = 4x + 4
f
-1
( x) = 2 x + 4
3
3) g( x) = g
-1
3
x+2
4) f ( x) = -
( x ) = - ( x - 2) 3
f
-1
3
1
+1
x+1
( x) = -
1
-1
x-1
Use compositions to determine if the functions are inverses.
5) f ( x) = -x + 5
g( x) = -x + 5
-25 - x
5
-9 - x
f ( x) =
3
6) g( x) =
Yes
No
3
7) h( x) = - x + 3
3
f ( x ) = - ( x - 3)
4
+2
x
4
g( x ) = x-2
8) f ( x) = -
Yes
Yes
Worksheet by Kuta Software LLC
-1-
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Find the inverse of each function. Then graph the function and its inverse. You may use a
calculator to help if necessary.
10) g( x) = x - 2
1
9) f ( x) = 1 + x
2
g
y
f
y
-1
( x) = x + 2
6
-1
( x) = 2x - 2
5
6
4
5
3
4
2
3
1
2
-6 -5 -4 -3 -2 -1
1
1
2
3
4
5
6 x
-1
-6 -5 -4 -3 -2 -1
1
2
3
4
5
6 x
-2
-1
-3
-2
-4
-3
-5
-4
-6
-5
-6
3
11) g( x) = 2x - 1
g
y
-1
( x) =
3
x+1
2
6
5
4
3
2
1
-6 -5 -4 -3 -2 -1
1
2
3
4
5
6 x
-1
-2
-3
-4
-5
-6
Perform the indicated operation.
12) g( x) = 4x + 3
h( x) = x 2 + 4x
Find ( g + h)( x)
13) h( x) = -x 3 + 3x 2
g( x ) = x + 2
Find (h - g)( x)
-x 3 + 3x 2 - x - 2
x 2 + 8x + 3
14) h(n) = -n - 5
g(n) = 2n + 5
Find (h × g)(n)
15) h( x) = 4x + 5
g( x) = x 2 - 5x
Find h( x) × g( x)
-2n 2 - 15n - 25
4x 3 - 15x 2 - 25x
Worksheet by Kuta Software LLC
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16) h(a) = a 3 - 4a
g(a) = 2a + 4
h
( a)
Find
g
()
17) g(a) = 3a + 4
f (a) = 4a + 5
Find ( g f )(3)
55
2
a - 2a
2
18) f ( x) = 2x + 3
g( x ) = x + 5
Find ( f g)(-9)
19) f ( x) = -4x + 3
g( x ) = x 2
Find ( f g)(2)
-5
20) g(n) = -n - 5
h(n) = 3n + 2
Find ( g h)(-5)
8
-13
21) h(n) = -2n - 2
g(n) = n 2 - 3n
n
Find (h g)
2
()
-4 - n 2 + 6n
2
22) f ( x) = x 3 - 5
g( x ) = x + 1
Find ( f g)(-4x)
23) g(n) = 3n - 2
f (n) = n 2 - 1
Find ( g f )(n)
-64x 3 + 48x 2 - 12x - 4
24) f (n) = n 3 - 5n
Find ( f f )(n)
n 9 - 15n 7 + 75n 5 - 130n 3 + 25n
3n 2 - 5
25) f (a) = 2a - 2
g( a) = a 3 - a 2
Find ( f g)(a - 2)
2a 3 - 14a 2 + 32a - 26
26) g(n) = n + 1
Find ( g g)(4n)
4n + 2
Worksheet by Kuta Software LLC
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Identify the domain and range of each. Then sketch the graph.
27) y =
x
28) y = 3
y
y
6
4
4
2
2
2
4
8 x
6
-8 -6 -4 -2
2
-2
-2
-4
-4
-6
-6
-8
-8
x+4
y
Domain: x ³ -4
Range: y £ 0
8
Domain: x ³ 0
Range: y ³ 0
8
6
-8 -6 -4 -2
29) y = -2
x
Domain: x ³ 0
Range: y ³ 0
8
30) y =
3
4
4
8 x
6
x+5+2
y
Domain: x ³ -5
Range: y ³ 2
8
6
6
4
4
2
2
-8 -6 -4 -2
2
4
8 x
6
-8 -6 -4 -2
-2
2
4
6
8 x
-2
-4
-4
-6
-6
-8
-8
31) y =
4x - 16 - 2
32) y = 2
y
x+4
y
Domain: x ³ 4
Range: y ³ -2
8
6
6
4
4
2
2
-8 -6 -4 -2
2
4
6
8 x
-8 -6 -4 -2
-2
-4
-4
-6
-6
y=-
8 x
y
8
8
6
6
4
4
2
2
-2
6
34) Write the equation of a square root
function with a starting point at (3, 4) and
passing through (-6,-5). SHOW
ALGEBRAIC WORK
y
-4
4
-8
33) Write the equation of a square root
function with a starting point at (-5, 7) and
passing through (-1,5). SHOW
ALGEBRAIC WORK
-6
2
-2
-8
-8
Domain: x ³ -4
Range: y ³ 0
8
2
4
6
8 x
-8
-6
-4
-2
2
-2
-2
-4
-4
-6
-6
-8
-8
4
6
8 x
y = -3 -( x - 3) + 4
x+5+7
Worksheet by Kuta Software LLC
-4-
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