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05 Apr 2025, 09:21
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
58% (01:47) correct
42%
(01:58)
wrong
based on 154
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Among the following functions, for which one is m(u^2 + v^2) = m(u^2) + m(v^2) for all integer values of u and v?
A. \(m(x) = x * \sqrt(3)\)
B. \(m(x) = (27x)^{(\frac{1}{3})}\)
C. \(m(x) = 3 + x\)
D. \(m(x) = \sqrt{9 + x}\)
E. \(m(x) = 3x^2\)
A. \(m(x) = x * \sqrt(3)\)
B. \(m(x) = (27x)^{(\frac{1}{3})}\)
C. \(m(x) = 3 + x\)
D. \(m(x) = \sqrt{9 + x}\)
E. \(m(x) = 3x^2\)
05 Apr 2025, 21:24
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We are tasked with determining which of the following functions satisfies the equation:
m(u2 + v2) = m(u2) + m(v2)
for all integer values of u and v. Let's analyze each function one by one.
Option A: m(x) = x * √3
[hr]
Option B: m(x) = (27x)^(1/3)
[hr]
Option C: m(x) = 3 + x
[hr]
Option D: m(x) = 9 + √x
[hr]
Option E: m(x) = 3x2
[hr]
Hence:
The only function that satisfies the equation for all integer values of u and v is:
m(u2 + v2) = m(u2) + m(v2)
for all integer values of u and v. Let's analyze each function one by one.
Option A: m(x) = x * √3
- Left-hand side: m(u2 + v2) = (u2 + v2) * √3
- Right-hand side: m(u2) + m(v2) = (u2) * √3 + (v2) * √3 = (u2 + v2) * √3
[hr]
Option B: m(x) = (27x)^(1/3)
- Left-hand side: m(u2 + v2) = (27(u2 + v2))^(1/3)
- Right-hand side: m(u2) + m(v2) = (27u2)^(1/3) + (27v2)^(1/3)
[hr]
Option C: m(x) = 3 + x
- Left-hand side: m(u2 + v2) = 3 + (u2 + v2) = 3 + u2 + v2
- Right-hand side: m(u2) + m(v2) = (3 + u2) + (3 + v2) = 6 + u2 + v2
[hr]
Option D: m(x) = 9 + √x
- Left-hand side: m(u2 + v2) = 9 + √(u2 + v2)
- Right-hand side: m(u2) + m(v2) = 9 + √(u2) + 9 + √(v2) = 18 + |u| + |v|
[hr]
Option E: m(x) = 3x2
- Left-hand side: m(u2 + v2) = 3(u2 + v2)2
- Right-hand side: m(u2) + m(v2) = 3u4 + 3v4
[hr]
Hence:
The only function that satisfies the equation for all integer values of u and v is:
- Option A: m(x) = x * √3
09 Apr 2025, 22:49
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I decided to take 2 and 3 as values for and u and test the equations for all option because it said any integers why is this wrong.
