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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
- e)None of these
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
If g is a real-valued function such that g(x) + 2g(1002/x) = 5x, where...
Solution: 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.
Most Upvoted Answer
If g is a real-valued function such that g(x) + 2g(1002/x) = 5x, where...
To find the value of g(3), we need to use the given equation and solve for g(x).
Given: g(x) * 2g(1002/x) = 5x
Let's substitute x = 1002/3 in the given equation to find g(1002/3):
g(1002/3) * 2g(3) = 5(1002/3)
Now, let's solve this equation to find g(1002/3):
2g(3) * g(1002/3) = 1670
Now, we need to find the value of g(3). To do that, we substitute x = 3 in the given equation:
g(3) * 2g(1002/3) = 5(3)
2g(1002/3) = 15/g(3)
Substituting this back into the previous equation, we get:
2g(3) * (15/g(3)) = 1670
2 * 15 = 1670
30 = 1670
This is not possible. Therefore, there is no real-valued function g(x) that satisfies the given equation. Hence, the correct answer is None of these (option E).
Given: g(x) * 2g(1002/x) = 5x
Let's substitute x = 1002/3 in the given equation to find g(1002/3):
g(1002/3) * 2g(3) = 5(1002/3)
Now, let's solve this equation to find g(1002/3):
2g(3) * g(1002/3) = 1670
Now, we need to find the value of g(3). To do that, we substitute x = 3 in the given equation:
g(3) * 2g(1002/3) = 5(3)
2g(1002/3) = 15/g(3)
Substituting this back into the previous equation, we get:
2g(3) * (15/g(3)) = 1670
2 * 15 = 1670
30 = 1670
This is not possible. Therefore, there is no real-valued function g(x) that satisfies the given equation. Hence, the correct answer is None of these (option E).
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