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02 Apr 2019, 16:28
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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%
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Question Stats:
60% (02:03) correct
40%
(02:32)
wrong
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Let be \(f(x) = \frac{2x}{{3x + 4}}\) and \(f(g(x)) = x\); then, \(g(x)\) will be equal to which of the following values?
A. \(\frac{3x + 4}{2x}\)
B. \(\frac{3x}{2x + 4}\)
C. \(\frac{2x + 4}{4x}\)
D. \(\frac{4x}{2 - 3x}\)
E. \(other\)
A. \(\frac{3x + 4}{2x}\)
B. \(\frac{3x}{2x + 4}\)
C. \(\frac{2x + 4}{4x}\)
D. \(\frac{4x}{2 - 3x}\)
E. \(other\)
02 Apr 2019, 22:24
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So the equation doesn't look too confusing, we can just let g(x) = k. Then
f(g(x)) = f(k) = 2k / (3k + 4)
The question tells us this equals x, so
2k / (3k + 4) = x
2k = 3kx + 4x
2k - 3kx = 4x
k(2 - 3x) = 4x
k = 4x / (2 - 3x)
And since k = g(x) is what we wanted to find, that's the answer.
f(g(x)) = f(k) = 2k / (3k + 4)
The question tells us this equals x, so
2k / (3k + 4) = x
2k = 3kx + 4x
2k - 3kx = 4x
k(2 - 3x) = 4x
k = 4x / (2 - 3x)
And since k = g(x) is what we wanted to find, that's the answer.
15 May 2019, 13:01
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The problem can be solved easily by taking X=1 and substitute the value of g(x) from option into f(x).
