Ch 6 Study Guide Answer Key
Learning Target 6B and 6C
5
3
1
5x 12 y 4
1.
3y
3
4
29
5 4 2 4 x 5 y 30
2.
2xy
3.
19
4.
1
1
2
63 x4 y 5
8
4
13
60x 20 y 20
5x 5 y 3
5.
x4
6.
√
3
xy 3x2
Learning Target 6E
1.
2x2 − 1
3x
x 6= 0
2. 21x
√
3. 3x 3x + 5
IR
x 6= 0
2
1
4. 7x 3 + 3x 3
x≥−
5
3
IR
1
5.
7x 3
3
x 6= 0
Learning Target 6E and 6F
1. x ≥ 4
5. x > 3
y≥3
2. x ≥ 3
x ≤ −3
3. x 6= −2
y 6= 5
y≥9
y≥8
6.x 6= 2
4. x 6= 6
x 6= 1
y 6= 2
y 6= 0
Learning Target 6F
√
8. 7 3 3x + 5
1
√
3 3x + 5
5
x>−
3
4
6. 98x 3 − 1
7.
IR
x≥−
5
3
Learning Target 6G - See graph page
Learning Target 6H
1. No Solution
(x = ±4 Extraneous)
5. x =
117
20
2. x = 0
(x = -7 Extraneous)
6. x =2
x=
3. x = 0, x =
10
9
1
2
7. x = 6
(x=1 Extraneous)
4. x = 0, 5, 1
Sorry we already did this one
8. No Solution
11
(x = 1, −
Extra25
neous)
Learning Target 6D
r
1. f −1 (x) =
x+3
4
2. g −1 (x) =
5. m−1 (x) =
6 − 2x
x
6.
p
x−5
3
n−1 (n(x))
(x +
−5
=x+5−5=x
5)2
3. h−1 (x) =
=
(x + 1)3
−3
8
−1
6. n(n
(x))
√
√
= ( x −√
5)2 + 10( x−)5
√ + 25
= x − 10 x + 25 + 10 x − 50 + 25
= x + 25 − 50 + 25 = x
4.k −1 (x)
3x − 10
4
=
Target 6G
−4
−3
−2
4
4
3
3
2
2
1
1
−1
−1
1
2
3
4 −5 −4 −3 −2 −1
−1
−2
−2
−3
−3
−4
−4
1
2
3
6
4
3
−11 −9
−7
6
7
−5
−3
−1
−1
−2
−3
−4
−5
−6
−7
1
3
1
2
3
4
5
2
1
−1
−1
5
8
4
3
2
1
5
−2
4
1
2
3
4
5
6
−2
8
4
7
3
6
2
5
1
4
−2
3
2
−1
−1
−2
1
−3
−5 −4 −3 −2 −1
−1
1
2
3
4
−4
6
Study Guide Problems
Inverse
2. g(x) = 3x2 + 5
4x + 10
4. k(x) =
3
1. f (x) = 4x − 3
√
3. h(x) = 2 3 x + 3 − 1
5. m(x) =
6
x+2
6.
Use Composite functions to verify if the functions are inverses
√
n(x) = x2 + 10x + 25
n−1 (x) = x − 5
Function Operations Find the Domain and Range of 4-6
f (x) = 2x2 − 1
g(x) =
1.
√
3x + 5
f (x) · h(x)
5.
h(x) =
2.
1
3x
k(x) · m(x)
k(x)
m(x)
1
2
m(x) = 3x 3
k(x) = 7x 3
g(x)
h(x)
3.
6. f (k(x))
7.
4. k(x) + m(x)
h(g(x))
8.
k(g(x))
Exponent Simplification
1.
2
1
1
4
3
4
1
5x 3 y 2
3x y
2.
4
5
5.
80x y 3
16x4 y
6.
1
3
1
20x 5 y 5
8xy
! 41
3.
1
3
2
3
1
1
(12x 5 y 4 )(5x 4 y 5 )
4.
3
6
1
(6x 4 y 5 ) 3
p
√
3
y 24x5 + x 3 −3x2 y 3
Domain and Range
√
1. y = 2 x − 4 + 3
2.
p
x2 − 9 + 9
4
+2
− 5x − 6
5.
∗ ∗√
4.
x2
7
+8
x−3
3.
6
+5
x+2
x2 + 6x
6.
x−2
Graph
√
x+3−2
√
4. k(x) = −3 3 x + 6
1. f (x) =
Solve Radicals
1
g(x) = (x − 4) 3 + 1
√
5. m(x) = 2 x + 2 + 2
2.
√
3. h(x) = − x − 1 + 4
2√
6. n(x) =
x+1−3
3
1.
2.
p
√
x2 + 9 + 3 = −2
x + 16 = x + 4
±4
NS
x = 0, −7
x=0
1
4x2 − 2x = 0
x = 0,
(6x + 1) = 2x + 1
2
p
3
4.
6x2 − 5x = x
x3 − 6x2 + 5x = 0
x = 0, 5, 1
√
5. − 2 5x + 1 + 5 = −6
9x2 − 35x + 24 = 0
(9x − 8)(x − 3) = 0
1
2
3.
6.
7.
8.
9.
√
4x + 1 =
√
x−1+2
√
8x + 1 + 5 = 2x
√
2 x + 3 = 1 − 5x
√
2x + 3 − 4 ≤ −5
√
3x − 2 = 4 x − 1
4x2 − 28x + 24 = 0
25x2 − 14x − 11 = 0
2x + 3 ≤ 1
9x2 − 28x + 20 = 0
x = 6, 1
3
2
8
9
(9x − 10)(x − 2) = 0
x=6
(25x + 11)(x − 1) = 0
x ≤ −1, x ≥ −
x = 3,
N oSol
x=−
11
,
25
x = 2,
10
9