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Argument of Composition

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rajlal
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Argument of Composition [#permalink] New post   Updated on: 15 Sep 2018, 02:40
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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
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D

Originally posted by rajlal on 15 Sep 2018, 01:46.
Last edited by rajlal on 15 Sep 2018, 02:40, edited 1 time in total.
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arjuntej3710
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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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