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Section 1.3: New Functions From Old Functions

1..png”>, then f(2x) is equal to a. .png”> e. .png”> b. .png”> f. .png”> c. .png”> g. .png”> d. .png”> h. .png”> 2. Let f(x) =.png”> and g(x)=.png”>. Find the…

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1..png”>, then f(2x) is equal to

a.

.png”>

e.

.png”>

b.

.png”>

f.

.png”>

c.

.png”>

g.

.png”>

d.

.png”>

h.

.png”>

2. Let f(x) =.png”> and g(x)=.png”>. Find the domains of.png”>.

a.

(.png”>Â¥, 0]

e.

[.png”>Â¥)

b.

(2,Â¥)

f.

(.png”>Â¥,.png”>)

c.

(.png”>Â¥, -2)

g.

(.png”>Â¥,.png”>].png”>[2,Â¥)

d.

(.png”>Â¥, 2).png”> (2,Â¥)

h.

.png”>

3. Let f(x) =.png”> and g(x)=.png”>. Find the domains of.png”>

a.

[1,Â¥)

e.

[.png”>3, 3]

b.

[.png”>.png”>,.png”>]

f.

(.png”>Â¥, -1].png”> [1,Â¥)

c.

(.png”>Â¥,.png”>.png”>].png”> [.png”>, Â¥)

g.

(.png”>Â¥, -1]

d.

(.png”>Â¥, -3].png”> [3,Â¥)

h.

[.png”>,Â¥)

4. Let h(x) = sin.png”>x.png”> 3 sin x.png”> 4 and g(x).png”> sin x. Find f(x)
so that h(x).png”>.png”>

a.

f(x) = (3x+ 2).png”>.png”>

e.

f(x) = 3x.png”>.png”> 4x

b.

f(x) = x+ 3

f.

f(x) = x.png”>.png”> 3x.png”>4

c.

f(x) = 3x.png”>.png”> 4

g.

f(x) = x.png”>.png”>4

d.

f(x) = x.png”>.png”> 3x.png”> 4

h.

f(x) = (x.png”>4).png”>

5. Let f(x) = 3x.png”> 2 and g(x).png”> 2.png”> 3x. Find the value of (f
° g)(x) when x= 3..

a.

.png”>23

e.

3

b.

.png”>9

f.

6

c.

.png”>6

g.

9

d.

.png”>3

h.

23

6. Let f(x) = 2.png”> x.png”> and g(x).png”> 3.png”> x. Find the value of.png”> when x=.png”>5.

a.

.png”>510

e.

5

b.

.png”>5

f.

10

c.

.png”>2

g.

127

d.

0

h.

130

7. Let f(x) =.png”>x and.png”>. Find g(2).

a.

0

e.

8

b.

1

f.

16

c.

2

g.

32

d.

4

h.

64

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