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The functions f(x) and g(x) are defined by f(x) = x^2 - 1 and g(x) = 1
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17 Sep 2018, 01:55
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Difficulty:
45% (medium)
Question Stats:
68% (01:56) correct 32% (02:07) wrong based on 68 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?
The functions f(x) and g(x) are defined by f(x) = x^2 - 1 and g(x) = 1
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Updated on: 17 Sep 2018, 18:53
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Bunuel 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?
A. 1/2 B. \(\frac{√3}{2}\) C. 1 D. 3/2 E. -1
\(f(g(k)) = 3\) or \(f(1-2k) = 3\) or \((1-2k)^2 -1 = 3\) or \((1-2k)^2 = 4\) or \(|1-2k| =2\) or \(k= -1/2\) or \(3/2\)............Ans D _________________
Please let me know if I am going in wrong direction. Thanks in appreciation.
Re: The functions f(x) and g(x) are defined by f(x) = x^2 - 1 and g(x) = 1
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17 Sep 2018, 10:08
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Bunuel 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?
A. 1/2
B. \(\frac{√3}{2}\)
C. 1
D. 3/2
E. -1
Looks like a great candidate for the something method (see video below)
We're told that f(g(k)) = 3
Let's let g(k) = something So, we have f(something) = 3
f(x) = x² - 1 So, f(something) = something² - 1 = 3 If something² - 1 = 3, then... something² = 4 This tells us that EITHER something = 2 OR something = -2 In other words, g(k) = 2 OR g(k) = -2
Let's test each case.
case 1) g(k)= 2 g(x) = 1 – 2x So, g(k) = 1 – 2k This means: 1 - 2k = 2 Subtract 1 from both sides: -2k = 1 Solve: k = -1/2 Check the answer choices.....NOT THERE! Looks like case 2 will yield the correct answer then.
case 2) g(k)= -2 This means: 1 - 2k = -2 Subtract 1 from both sides: -2k = -3 Solve: k = (-3/(-2) = 3/2 Check the answer choices..... Answer: D