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Argument of Composition

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Intern
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Joined: 22 Aug 2018
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Argument of Composition [#permalink] New post 15 Sep 2018, 01:46
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Question Stats:

63% (01:19) correct 36% (01:32) wrong based on 11 sessions
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.\(-1\)
[Reveal] Spoiler: OA

Last edited by rajlal on 15 Sep 2018, 02:40, edited 1 time in total.
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Re: Argument of Composition [#permalink] New post 15 Sep 2018, 02:01
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Re: Argument of Composition [#permalink] New post 15 Sep 2018, 06:01
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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?



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
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Re: Argument of Composition   [#permalink] 15 Sep 2018, 06:01
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Argument of Composition

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