practice problems: the composition of functions
DESCRIPTION
Practice Problems: The Composition of Functions Work problems on your own first. Then check with answers in the following slides. If the answers don’t help, complete solutions are available in the final slides. Use the graphs of y = f(x) and y = g(x) to find each of the following - PowerPoint PPT PresentationTRANSCRIPT
Practice Problems: The Composition of FunctionsWork problems on your own first. Then check with answers in thefollowing slides. If the answers don’t help, complete solutions areavailable in the final slides.
1. Given 2)( xxf and xxg 3)( , find
a. ).5)(( gf b. )5)(( fg c. ))(( xgf d. ))(( xfg
2. Given 22)( xxxf and 43)( xxg , find
))((.
))((.
)2)((.
)2)((.
xfgd
xgfc
fgb
gfa
3. Given 24)( xxxf and 2)( xxg , find
a. )3)(( gf b. )3)(( fg c. ))(( xgf d. ))(( xfg
4. Given 6)( 2 xxf and xxg 5)( , find
))((.
))((.
)1)((.
)1)((.
xfgd
xgfc
fgb
gfa
5. Given xxf
2
2)( and
2)( xxg
))((.
))((.
)4)((.
)4)((.
xfgd
xgfc
fgb
gfa
6. Given 5)( 2xxf and 5)( xxg , find a. )6)(( gf b. )6)(( fg c. ))(( xgf d. ))(( xfg
7. Given 62)( xxf and xxg )( , find
))((.
))((.
))9((.
))9((.
xfgd
xgfc
fgb
gfa
8. Given xxf
2)( and xxg 4)(
))((.
))((.
))4((.
))4((.
xfgd
xgfc
fgb
gfa
-4 -3 -2 -1 1 2 3 4
-4
-3
-2
-1
1
2
3
4
y = f(x)y = g(x)
Use the graphs of y = f(x) and y = g(x) to find each of the followingcompositions.
a. f(g(3))
b. g(f(3))
c. f(g(0))
d. g(f(0))
e. g(g(3))
Answers to Practice Problems for Composition of Functions(Complete solutions follow.)
1. a. 4 b. –22
2
2
3.
)3(.
xd
xc
463.
16269.
4.
0..2
2
2
xxd
xxc
b
a
2
2
11.
1.
10.
2..4
24.
224.
1.
3..3
xd
xc
b
a
xxd
xxc
b
a
Answers to Practice Problems for Composition of Functions(Complete solutions follow.)
xd
xc
b
a
xd
xc
b
a
.
.
6.
6..6
2
2.
2
2.
1.7
1..5
2
2
2
2
4.
4.
12.
0..8
26.
62.
6224.
0..7
xd
xc
b
a
xd
xc
b
a
9. a. –5 b. –1 c. 4 d. 2 e. 3
Complete solutions to Practice Problems for Composition ofFunctions.
463436
423)2())(()(.
16269162492
)43(2)43())(()(.
4)0())2(()2(.
044)2())2((2.
43)(,2)(.2
3)())(()(.
3)3())((.
22253)25())5((5.
2)2())5((5.
3)(,)(.1
22
22
22
2
2
22
2
2
2
xxxx
xxxxgxfgxfgd
xxxxx
xxxfxgfxgfc
gfgfgb
fgfgfa
xxgxxxf
xxgxfgxfgd
xxfxgfxgfc
gfgfgb
fgfgfa
xxgxxf
Complete solutions to Practice Problems for Composition ofFunctions.
222
2
22
1165)6())((.
165)5())((.
1055)5()1((1.
264)2())1((1.
5)(,6)(.4
244.
165)5(.
1123)3())3((3.
314)1())3((3..3
xxxgxfgxfgd
xxxfxgfxgfc
gfgfgb
fgfgfa
xxgxxf
xxxxgxfgd
xxxfxgfc
gfgfgb
fgfgfa
Complete solutions to Practice Problems for Composition ofFunctions.
xxxxgxfgxfgd
xxxfxgfxgfc
gfgfgb
fgfgfa
xxgxxf
xxxgxfgxfgd
xxfxgfxgfc
gfgfgb
fgfgfa
xxgx
xf
222
2
222
22
2
2
5)5()5())(())((.
5)5(5))(())((.
636)41())6(()6)((.
6)1())6(()6)((.
5)(,5)(.6
11656))(())((.
2
2)())(())((.
1)1()1())4(()4(.
7
1
162
2)16())4(()4)((.
)(,2
2)(.5
Complete solutions to Practice Problems for Composition ofFunctions.
22
2
2
4)())((.
4)4())((.
12164)16())4((.
0)0())4((.
4)(,)(.8
2662)62())((.
62)())((.
6264)24()24())9((.
0)3()9())9((.
5)(,5)(.7
xxgxfgd
xxfxgfc
gfgb
fgfa
xxgxxf
xxxgxfgd
xxfxgfc
gfgb
ffgfa
xxgxxf
-4 -3 -2 -1 1 2 3 4
-4
-3
-2
-1
1
2
3
4
y = f(x)y = g(x)
Use the graphs of y = f(x) and y = g(x) to find each of the followingcompositions.
a. f(g(3))=
f(-1) = -5
b. g(f(3))=
g(3) = -1
c. f(g(0))=
f(2) = 4
d. g(f(0)) =
g(0) = 2
e. g(g(3) =
g(-1) = 3