Chapter 9 Radical Functions

SSM: Intermediate Algebra Homework 9.5
57. ( x + 3)( x + 1)
x ⋅ x + 3⋅ x + x ⋅ 1+ 3⋅1
x + 3 x + x + 3
x + 4 x + 3
59. f ( x) = 5 x − 7
5 x − 7 = 0
x − 7 = 0
( ) 2 2
x − 7 = 0
x − 7 = 0
x = 7
Check x = 7
( )
?
5 7 − 7 = 0
0 = 0 true
7,0 .
The x-intercept is ( )
= − + −
61. h( x) 3 3x
4 15
3 − 3x
+ 4 − 15 = 0
3 − 3x
+ 4 = 15
− 3x
+ 4 = 5
( ) 2 2
− 3x
+ 4 = 5
− 3x
+ 4 = 25
− 3x
= 21
x = −7
Check x = − 7
( )
3 −3 − 7 + 4 − 15=
0
?
0 = 0 true
− 7,0 .
The x-intercept is ( )
63. f ( x) = 3x − 2 − x + 8
3x
− 2 − x + 8 = 0
3x
− 2 = x + 8
( 3x
− 2) = ( x + 8)
Check x = 5
( ) ( )
2 2
3x
− 2 = x + 8
2x
= 10
x = 5
3 5 − 2 − 5 + 8 = 0
?
0 = 0 true
The x-intercept is ( 5,0 ).
65. h( x) = 2 x + 4 + 3 x − 5
2 x + 4 + 3 x − 5 = 0
Check
2 x + 4 = −3 x − 5
( 2 x + 4) = ( −3 x − 5)
x =
2 2
( x + ) = ( x − )
4 4 9 5
4x
+ 16 = 9x
− 45
61
5
− 5x
= −61
x =
61
5
?
⎛ 61⎞ ⎛ 61⎞
2 ⎜ ⎟ + 4 + 3 ⎜ ⎟ − 5 = 0
⎝ 5 ⎠ ⎝ 5 ⎠
36
?
= 0 false
5
No real number solution. There are no
x-intercepts.
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