Consider the following sets.
1 answer:
Answer:
[2,3] is the answer
assuming you didn't have equal symbols under the inequality signs, you know and
.
Step-by-step explanation:
Ok let's solve 3x+4>13 or 1/2 x+3<4.
Let's begin with 3x+4>13.
3x+4>13
Subtract 4 on both sides:
3x>9
Divide both sides by 3:
x>3
Now the other 1/2 x +3<4.
Subtract 3 on both sides:
1/2 x<1
Multiply both sides by 2:
x<2
So we have x>3 or x<2
If we graph this, this will give us better idea of what is and isn't a solution.
~~~~~~~~O x<2
O~~~~~~ x>3
------------(2)---------(3)---------
The only numbers not included are between 2 and 3 (inclusive).
So if x is between [2,3] then A or B has no solution.
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Answer:
a. 2^(x-2) = g^(-1)(x)
b. A, B, D
Step-by-step explanation:
the phrasing attached in the image is flagged as inappropriate, so i will be replacing it with g(x) and its inverse with g^(-1)(x)
1. replace g(x) with y and solve for x
y = log₂(x) + 2
subtract 2 from both sides to isolate the x and its log
y - 2 = log₂(x)
this text is replaced by the second image -- it was marked as inappropriate
thus, 2^(y-2) = x
replace x with g^(-1)(x) and y with x
2^(x-2) = g^(-1)(x)
2. plug this in to points A, B, C, D, E, and F
A: (2,1)
plug 2 in for x
2^(2-2) = 2⁰ = 1 so this works
B: (4, 4)
2^(4-2) = 2²= 4 so this works
C: (9, 3)
2^(9-2) = 2⁷ = 128 ≠ 3 so this doesn't work
(5, 8)
2^(5-2) = 2³ = 8 so this works
E: (3, 5)
2^(3-2) = 2¹ = 2 ≠ 5 so this doesn't work
F: (8, 5)
2^(8-2) = 2⁶ = 64 ≠ 5 so this doesn't work
