Unit 10 Take Home Review
Name___________________________________
Solve the problem.
1) Find f(-3) when f(x) = x2 - 4x - 2
A) 19
B) -1
1)
C) -5
D) 23
2) Find g(a + 1) when g(x) = 1 x + 4.
2
A)
a-9
2
B)
2)
1a-2
2
C)
Perform the requested operation or operations.
3) f(x) = 8x - 5, g(x) = 2x - 6
Find (f - g)(x).
A) 6x - 11
B) -6x - 1
1a+4
2
D)
a+9
2
3)
C) 6x + 1
D) 10x - 11
4) f(x) = 2x2 - 9x, g(x) = x2 - 3x - 54
f
Find
(x).
g
A)
2-x
54
B)
5) f(x) = 3 - 2x, g(x) = -8x + 2
Find (f + g)(x).
A) 6x + 5
6) f(x) = 3x + 2, g(x) =
Find (fg)(x).
A) (3x + 2)(3x - 4)
C) (3x + 2)(9x - 16)
4)
2x - 9
-3
C)
2x
x+1
D)
2x2 - 9x
x2 - 3x - 54
5)
B) -8x + 3
C) -10x + 5
D) -5x
9x - 16
7) f(x) = 3x + 5, g(x) = 2x - 1
Find (f ∘ g)(x).
A) 6x + 4
6)
B) (3x - 4)( 3x + 2)
D) ( 3x + 2)( 9x - 16)
7)
B) 6x + 2
C) 6x + 8
8) f(x) = 4x2 + 6x + 3, g(x) = 6x - 5
D) 6x + 9
8)
Find (g ∘ f)(x).
A) 4x2 + 36x + 13
B) 24x2 + 36x + 13
D) 24x2 + 36x + 23
C) 4x2 + 6x - 2
1
Find the domain and range of the indicated function.
9) Find the domain and range of (fg)(x) when f(x) =
4
A) Domain: - , ∞ ; range: (-∞, ∞)
7
C) Domain:
9x + 5 and g(x) = 7x - 4.
4
B) Domain:
, ∞ ; range: (-∞, ∞)
7
4
, ∞ ; range: [0, ∞)
7
D) Domain:
4
, ∞ ; range: (0, ∞)
7
Find the requested value.
10) The graphs of functions f and g are shown. Use these graphs to find f(1) * g(1).
y
10)
y
5x
y = f(x)
A) -3
9)
5x
y = g(x)
B) 2
C) -4
D) -
1
3
11) Using the given tables find (g∘f) (9)
11)
x
9 12 10 20
f(x) 10 18 49 51
x
11 20 9 10
g(x) 21 17 20 19
A) 19
B) 17
Find the indicated composite for the pair of functions.
12) (f ∘ g)(x): f(x) = 3x + 13, g(x) = 4x - 1
A) 12x + 12
B) 12x + 10
C) 9
D) 49
C) 12x + 51
D) 12x + 16
12)
13) (g ∘ f)(x): f(x) = 4x2 + 4x + 8, g(x) = 4x - 5
A) 4x2 + 4x + 3
13)
B) 16x2 + 16x + 37
D) 4x2 + 16x + 27
C) 16x2 + 16x + 27
2
Determine whether the function is invertible. If it is invertible, find the inverse.
14) {(15, -20), (-13, -2), (18, -4)}
A) {(15, -2), (15, -13), (-4, 18)}
B) {(-20, 15), (-2, -13), (-4, 18)}
C) {(-20, 15), (18, -13), (-4, -2)}
D) Not invertible
Use the horizontal line test to determine whether the function is one-to-one.
15)
14)
15)
y
10
5
-10
-5
5
10
x
-5
-10
A) Yes
B) No
16)
16)
y
10
5
-10
-5
5
10
x
-5
-10
A) No
B) Yes
Find the inverse of the function.
17) f(x) = x - 6
7
17)
A) f-1(x) = x + 13
C) f-1(x) = 7x + 42
B) f-1(x) = 7x - 42
D) f-1(x) = 7x + 6
18) f(x) =
x+ 6
A) f-1(x) = -x2 + 6 for x ≥ 0
C) f-1(x) = x2 - 36 for x ≥ 0
18)
B) f-1(x) = x2 - 6 for x ≥ 0
D) Not invertible
3
Decide whether or not the functions are inverses of each other.
19) f(x) = 7x - 4, g(x) = x + 7
4
A) Yes
19)
B) No
Decide whether the two functions represented by the solid curves are inverses of each other.
20)
20)
y
x
A) Yes
B) No
21)
21)
y
x
A) Yes
B) No
Graph the inverse of the function plotted, on the same set of axes. Use a dashed curve for the inverse.
22)
22)
y
10
10 x
-10
-10
4