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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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Joined: 02 Sep 2009
Posts: 58409
The functions f(x) and g(x) are defined by f(x) = x^2 - 1 and g(x) = 1  [#permalink]

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17 Sep 2018, 01:55
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Difficulty:

45% (medium)

Question Stats:

69% (01:56) correct 31% (02:05) wrong based on 73 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?

A. 1/2

B. $$\frac{√3}{2}$$

C. 1

D. 3/2

E. -1

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The functions f(x) and g(x) are defined by f(x) = x^2 - 1 and g(x) = 1  [#permalink]

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Updated on: 17 Sep 2018, 18:53
2
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
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Originally posted by u1983 on 17 Sep 2018, 08:15.
Last edited by u1983 on 17 Sep 2018, 18:53, edited 1 time in total.
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Joined: 12 Sep 2015
Posts: 4007
Re: The functions f(x) and g(x) are defined by f(x) = x^2 - 1 and g(x) = 1  [#permalink]

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17 Sep 2018, 10:08
Top Contributor
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
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

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Re: The functions f(x) and g(x) are defined by f(x) = x^2 - 1 and g(x) = 1  [#permalink]

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17 Sep 2018, 13:52
1
f(g(k)) = 3

f(x) = x²-1 = 3 -> x² = 4 -> x = 2 or -2

If x = 2
g(x) = 1 - 2*x = 2 -> x = -1/2

If x = -2
g(x) = 1 - 2*k = -2 -> x = 3/2

Re: The functions f(x) and g(x) are defined by f(x) = x^2 - 1 and g(x) = 1   [#permalink] 17 Sep 2018, 13:52
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