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Argument of Composition
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Updated on: 15 Sep 2018, 02:40
Updated on: 15 Sep 2018, 02:40
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Question Stats:
78% (01:34) correct
21% (01:29) wrong based on 28 sessions
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The functions \(f(x)\) and \(g(x)\) are defined by \(f(x) = x^2 – 1\) and \(g(x) = 1 – 2x\). Given that \(f(g(k)) = 3\), which of the following could be the value of k?
Options
A. \(\frac{1}{2}\)
B. \(\frac{√3}{2}\)
C. \(1\)
D. \(\frac{3}{2}\)
E.\(-1\)
Options
A. \(\frac{1}{2}\)
B. \(\frac{√3}{2}\)
C. \(1\)
D. \(\frac{3}{2}\)
E.\(-1\)
Re: Argument of Composition
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15 Sep 2018, 06:01
15 Sep 2018, 06:01
1
rajlal wrote:
The functions \(f(x)\) and \(g(x)\) are defined by \(f(x) = x^2 – 1\) and \(g(x) = 1 – 2x\). Given that \(f(g(k)) = 3\), which of the following could be the value of k?
Options
A. \(\frac{1}{2}\)
B. \(\frac{√3}{2}\)
C. \(1\)
D. \(\frac{3}{2}\)
E.\(-1\)
Why does the method of substitution give me the wrong answer?
Options
A. \(\frac{1}{2}\)
B. \(\frac{√3}{2}\)
C. \(1\)
D. \(\frac{3}{2}\)
E.\(-1\)
Why does the method of substitution give me the wrong answer?
Given \(f(x) = x^2 - 1\) and \(g(x)= 1 - 2x\)
Now
\(g(k) = 1 - 2k\)
\(f(g(k)) = (1 - 2k)^2 - 1\)
But \(f(g(k)) = 3\)
so,
\(3 = (1 - 2k)^2 - 1\)
or \(4k^2 - 4k - 3 = 0\)
or \(4k^2 -6k + 2k - 3 = 0\)
or \(k^2 - \frac{3k}{2} +\frac{k}{2} - \frac{3}{4} = 0\)
or \((k - \frac{3}{2})(k +\frac{1}{2}) = 0\)
we get \(k = -\frac{1}{2} or \frac{3}{2}\)
Only Option D is correct
