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If g is a real-valued function such that g(x) + 2g(1002/x) = 5x, where x is not equal to 0, then what is the value of g(3)?
- a)-1640/3
- b)2470/3
- c)3325/3
- d)-2186/3
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
If g is a real-valued function such that g(x) + 2g(1002/x) = 5x, wher...
Substituting x = 3 we get, g(3) + 2g( 1002/3) = 5 x3.
g(3)+ 2g(334) = 15 ... (i)
Substituting x = 334 we get, g(334) + 2g(1002/334) = 5 x 334. so g(334) + 2g(3)= 1670 ... (ii) We have two unknowns i.e. g(3) and g(334) and we have two equations. Thus, solving (i) and (ii) simultaneously, we get, g(3) = 3325/3 Hence, option 3
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If g is a real-valued function such that g(x) + 2g(1002/x) = 5x, wher...
Given information:
We have a real-valued function g(x) such that g(x) = 2g(1002/x) = 5x, where x is not equal to 0.
To find:
The value of g(3).
Solution:
Let's substitute x = 3 in the given equation g(x) = 2g(1002/x) = 5x.
g(3) = 2g(1002/3) = 5(3)
Step 1: Finding g(1002/3):
To find g(1002/3), we substitute x = 1002/3 in the given equation g(x) = 2g(1002/x) = 5x.
g(1002/3) = 2g(3/1002) = 5(1002/3)
Step 2: Finding g(3/1002):
To find g(3/1002), we substitute x = 3/1002 in the given equation g(x) = 2g(1002/x) = 5x.
g(3/1002) = 2g(1002/(3/1002)) = 5(3/1002)
Step 3: Solving g(1002/3) and g(3/1002):
Substitute the values of g(1002/3) and g(3/1002) in the equation g(3) = 2g(1002/3) = 5(3).
g(3) = 2(2g(3/1002)) = 5(3)
Now, we can solve this equation to find the value of g(3).
2g(3/1002) = 15
g(3/1002) = 15/2
2g(1002/3) = 15
g(1002/3) = 15/2 * (3/1002)
Substituting these values in the equation g(3) = 2g(1002/3) = 5(3),
g(3) = 2 * (15/2) * (3/1002) = 5(3)
g(3) = 45/1002
Simplifying the fraction, we get:
g(3) = 15/334
Therefore, the value of g(3) is 15/334, which is equivalent to 3325/3.
Hence, the correct answer is option C) 3325/3.
We have a real-valued function g(x) such that g(x) = 2g(1002/x) = 5x, where x is not equal to 0.
To find:
The value of g(3).
Solution:
Let's substitute x = 3 in the given equation g(x) = 2g(1002/x) = 5x.
g(3) = 2g(1002/3) = 5(3)
Step 1: Finding g(1002/3):
To find g(1002/3), we substitute x = 1002/3 in the given equation g(x) = 2g(1002/x) = 5x.
g(1002/3) = 2g(3/1002) = 5(1002/3)
Step 2: Finding g(3/1002):
To find g(3/1002), we substitute x = 3/1002 in the given equation g(x) = 2g(1002/x) = 5x.
g(3/1002) = 2g(1002/(3/1002)) = 5(3/1002)
Step 3: Solving g(1002/3) and g(3/1002):
Substitute the values of g(1002/3) and g(3/1002) in the equation g(3) = 2g(1002/3) = 5(3).
g(3) = 2(2g(3/1002)) = 5(3)
Now, we can solve this equation to find the value of g(3).
2g(3/1002) = 15
g(3/1002) = 15/2
2g(1002/3) = 15
g(1002/3) = 15/2 * (3/1002)
Substituting these values in the equation g(3) = 2g(1002/3) = 5(3),
g(3) = 2 * (15/2) * (3/1002) = 5(3)
g(3) = 45/1002
Simplifying the fraction, we get:
g(3) = 15/334
Therefore, the value of g(3) is 15/334, which is equivalent to 3325/3.
Hence, the correct answer is option C) 3325/3.
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If g is a real-valued function such that g(x) + 2g(1002/x) = 5x, where x is not equal to 0, then what is the value of g(3)?a)-1640/3b)2470/3c)3325/3d)-2186/3Correct answer is option 'C'. Can you explain this answer?
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