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A function a(x) is defined for x as 3a(x) + 2a (2 – x) = (x + 3)2. What is the value of [G (–5)]
where [x] represents the greatest integer less than or equal to x?
- a)37
- b)–38
- c)–37
- d)Cannot be determined
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A function a(x) is defined for x as 3a(x) + 2a (2 – x) = (x + 3)...
The equation given in the question is: 3a(x) + 2a (2–x) = (x + 3)2
Replacing x by (2–x) in the above equation, we get
3a(2–x) + 2a(x) = (5–x)2
Solving the above pairs of equation, we get
a(x) = (x2 + 38 – 23)/5
Thus, G(–5) = –188/5 = –37.6. The value of [–37.6] = –37. Hence, Option (c) is the correct
answer.
Replacing x by (2–x) in the above equation, we get
3a(2–x) + 2a(x) = (5–x)2
Solving the above pairs of equation, we get
a(x) = (x2 + 38 – 23)/5
Thus, G(–5) = –188/5 = –37.6. The value of [–37.6] = –37. Hence, Option (c) is the correct
answer.
Most Upvoted Answer
A function a(x) is defined for x as 3a(x) + 2a (2 – x) = (x + 3)...
Given equation: 3a(x) - 2a(2x) = (x - 3)^2
To find the value of [G(5)], we need to substitute x = 5 in the equation and then find the value of the expression.
Substituting x = 5 in the equation:
3a(5) - 2a(2*5) = (5 - 3)^2
3a(5) - 2a(10) = 2^2
3a(5) - 2a(10) = 4
Let's simplify the equation step by step:
1. Simplifying the term 2a(10):
We know that [x] represents the greatest integer less than or equal to x. So, [10] = 10.
So, 2a(10) = 2a(10) = 20
2. Substituting the value of 2a(10) in the equation:
3a(5) - 20 = 4
3. Adding 20 to both sides of the equation:
3a(5) = 4 + 20
3a(5) = 24
4. Dividing both sides of the equation by 3:
a(5) = 24/3
a(5) = 8
Now, we need to find the value of [G(5)]. Since 5 is an integer, [5] will be equal to 5 itself.
Therefore, [G(5)] = 5
The correct answer is option C) 37.
To find the value of [G(5)], we need to substitute x = 5 in the equation and then find the value of the expression.
Substituting x = 5 in the equation:
3a(5) - 2a(2*5) = (5 - 3)^2
3a(5) - 2a(10) = 2^2
3a(5) - 2a(10) = 4
Let's simplify the equation step by step:
1. Simplifying the term 2a(10):
We know that [x] represents the greatest integer less than or equal to x. So, [10] = 10.
So, 2a(10) = 2a(10) = 20
2. Substituting the value of 2a(10) in the equation:
3a(5) - 20 = 4
3. Adding 20 to both sides of the equation:
3a(5) = 4 + 20
3a(5) = 24
4. Dividing both sides of the equation by 3:
a(5) = 24/3
a(5) = 8
Now, we need to find the value of [G(5)]. Since 5 is an integer, [5] will be equal to 5 itself.
Therefore, [G(5)] = 5
The correct answer is option C) 37.
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A function a(x) is defined for x as 3a(x) + 2a (2 – x) = (x + 3)2. What is the value of [G (–5)]where [x] represents the greatest integer less than or equal to x?a)37b)–38c)–37d)Cannot be determinedCorrect answer is option 'C'. Can you explain this answer?
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