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22 Oct 2020, 12:51
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C
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Question Stats:
76% (01:52) correct
24%
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Given \(f(x) = \frac{2x}{2x − 1}\) and \(g(x) = \frac{2x − 1}{2x}\), for what value of x, does \(f(g(x)) = 3\)?
A. 0
B. 1
C. 2
D. 3
E. 4
A. 0
B. 1
C. 2
D. 3
E. 4
yashikaaggarwal
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22 Oct 2020, 13:04
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Given: F(x) = 2x/(2x-1)
G(x) = (2x-1)/2x
To find: For what value of X, F(g(x)) = 3
Solution: Putting value of g(x)
F(2x-1/2x) => 2(2x-1/2x) / 2(2x-1/2x)-1 = 3
2(2x-1/2x) = [2(2x-1/2x)-1]*3
2x-1/x = [2x-1/x - 1]*3
2x-1/x = [2x-1-x/x]*3
2x-1/x = [X-1/x]*3
2x-1 = 3x-3
-1+3 = 3x-2x
2 = X
Answer is C
Posted from my mobile device
G(x) = (2x-1)/2x
To find: For what value of X, F(g(x)) = 3
Solution: Putting value of g(x)
F(2x-1/2x) => 2(2x-1/2x) / 2(2x-1/2x)-1 = 3
2(2x-1/2x) = [2(2x-1/2x)-1]*3
2x-1/x = [2x-1/x - 1]*3
2x-1/x = [2x-1-x/x]*3
2x-1/x = [X-1/x]*3
2x-1 = 3x-3
-1+3 = 3x-2x
2 = X
Answer is C
Posted from my mobile device
22 Oct 2020, 15:25
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Bunuel
We may simplify the functions a bit before proceeding.
\(f(x) = \frac{(2x - 1) + 1}{2x - 1} = 1 + \frac{1}{2x - 1}\)
\(g(x) = 1 - \frac{1}{2x}\).
Then \(f(g(x)) = f(1 - \frac{1}{2x}) = 1 + \frac{1}{2*(1 - \frac{1}{2x}) - 1} = 1 + \frac{1}{1 - \frac{1}{x}} = 3\)
\(\frac{1}{1 - \frac{1}{x}} = 2\)
\(1 - \frac{1}{x} = \frac{1}{2}\)
\(\frac{1}{x} = \frac{1}{2}\) therefore \(x =2\).
Ans: C
