Write each fraction or mixed number as a decimal 2 3/4?
2 answers:
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<span>
Solving:
1)
-58 - 6x = 42 + 4x
</span>Pass the numbers with letter to the left and the numbers without letter to the right, changing the signal as they change sides.
<span>- 6x - 4x = 42 + 58
- 10x = 100 simplify by (-1)
10x = - 100
</span>
<span>
2)
37 + 5x = -2x - 33
</span>Pass the numbers with letter to the left and the numbers without letter to the right, changing the signal as they change sides.
<span>5x + 2x = - 33 - 37
7x = - 70
</span>
<span>
3)
27 - 9x = -6x - 39
</span>Pass the numbers with letter to the left and the numbers without letter to the right, changing the signal as they change sides.
- 9x + 6x = - 39 - 27
- 3x = - 66 simplify by (-1)
3x = 66
Solving:
1)
-58 - 6x = 42 + 4x
</span>Pass the numbers with letter to the left and the numbers without letter to the right, changing the signal as they change sides.
<span>- 6x - 4x = 42 + 58
- 10x = 100 simplify by (-1)
10x = - 100
</span>
2)
37 + 5x = -2x - 33
</span>Pass the numbers with letter to the left and the numbers without letter to the right, changing the signal as they change sides.
<span>5x + 2x = - 33 - 37
7x = - 70
</span>
<span>
3)
27 - 9x = -6x - 39
</span>Pass the numbers with letter to the left and the numbers without letter to the right, changing the signal as they change sides.
- 9x + 6x = - 39 - 27
- 3x = - 66 simplify by (-1)
3x = 66
Given:
g(x) = (1/3)x + 2
Part (a)
To find the inverse:
Set y = g(x) = (1/3)x + 2
Swap x and y.
x = (1/3)y + 2.
Solve for y.
(1/3)y = x - 2
y = 3(x - 2).
Set g⁻¹(x) to y.
Answer: g⁻¹(x) = 3(x - 2)
Part (b)
Create the table shown below to graph g(x) and g⁻¹(x).
x g(x) g⁻¹(x)
---- --------- ---------
-8 - 2/3 - 30
-6 0 - 24
-4 2/3 - 18
-2 4/3 - 12
0 2 - 6
2 8/3 0
4 4/3 6
6 4 12
8 14/3 18
Note that when x = -6, g(x) = 0, so that (-6, 0) lies on he black liine.
Therefore the inverse function should yield (0, -6) to be correct. This is so, so g⁻¹ is correct.
Both g(x) and g⁻¹(x)satisfy the vertical line test, so both are functions.
Part (c)
Algebraically, we know that g⁻¹(x) is correct if g(g⁻¹(x)) = x
Use function composition to obtain
g(g⁻¹(x)) = (1/3)*(3x - 6) + 2
= x - 2 + 2
= x
Therefore g⁻¹(x) is correct.
g(x) = (1/3)x + 2
Part (a)
To find the inverse:
Set y = g(x) = (1/3)x + 2
Swap x and y.
x = (1/3)y + 2.
Solve for y.
(1/3)y = x - 2
y = 3(x - 2).
Set g⁻¹(x) to y.
Answer: g⁻¹(x) = 3(x - 2)
Part (b)
Create the table shown below to graph g(x) and g⁻¹(x).
x g(x) g⁻¹(x)
---- --------- ---------
-8 - 2/3 - 30
-6 0 - 24
-4 2/3 - 18
-2 4/3 - 12
0 2 - 6
2 8/3 0
4 4/3 6
6 4 12
8 14/3 18
Note that when x = -6, g(x) = 0, so that (-6, 0) lies on he black liine.
Therefore the inverse function should yield (0, -6) to be correct. This is so, so g⁻¹ is correct.
Both g(x) and g⁻¹(x)satisfy the vertical line test, so both are functions.
Part (c)
Algebraically, we know that g⁻¹(x) is correct if g(g⁻¹(x)) = x
Use function composition to obtain
g(g⁻¹(x)) = (1/3)*(3x - 6) + 2
= x - 2 + 2
= x
Therefore g⁻¹(x) is correct.