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# f(x)=x^2 and g(x)=x−3. For which value of the following is g(f(x)) a

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Joined: 02 Sep 2009
Posts: 54376
f(x)=x^2 and g(x)=x−3. For which value of the following is g(f(x)) a  [#permalink]

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09 Feb 2017, 03:20
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15% (low)

Question Stats:

77% (01:20) correct 23% (01:34) wrong based on 186 sessions

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f(x)=x^2 and g(x)=x−3. For which value of the following is g(f(x)) a perfect square:

A. -2
B. -1
C. 1
D. 3
E. 4

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Joined: 17 May 2015
Posts: 249
Re: f(x)=x^2 and g(x)=x−3. For which value of the following is g(f(x)) a  [#permalink]

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09 Feb 2017, 03:37
1
Bunuel wrote:
f(x)=x^2 and g(x)=x−3. For which value of the following is g(f(x)) a perfect square:

A. -2
B. -1
C. 1
D. 3
E. 4

Hi,

Given: $$f(x) = x^{2}$$, and $$g(x) = x - 3$$.

So, $$g \left( f(x) \right) = g \left( x^{2} \right) = x^{2} - 3$$

Now, evaluate for each option.
(A) x = -2; $$x^{2} - 3$$ = 4 - 3 =1. One is a perfect square. Answer (A).

Thanks.
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Re: f(x)=x^2 and g(x)=x−3. For which value of the following is g(f(x)) a  [#permalink]

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13 Feb 2017, 17:10
Bunuel wrote:
f(x)=x^2 and g(x)=x−3. For which value of the following is g(f(x)) a perfect square:

A. -2
B. -1
C. 1
D. 3
E. 4

We are given that f(x)=x^2 and g(x)=x−3. We need to determine for which value of x is g(f(x)) a perfect square.

Let’s plug in each answer choice:

A) x = -2

f(-2) = (-2)^2 = 4

g(4) = 4 - 3 = 1

Since 1 is a perfect square, answer choice A is correct.

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Joined: 02 Sep 2016
Posts: 663
Re: f(x)=x^2 and g(x)=x−3. For which value of the following is g(f(x)) a  [#permalink]

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03 Apr 2017, 06:51
For what value of x, will x^2-3 be a perfect square?

Only option A.
(-2)^2-3= 4-3=1

Properties of 1:
(1) 1 is a perfect square (1^2=1)
(2) Square root of 1 is 1.
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Re: f(x)=x^2 and g(x)=x−3. For which value of the following is g(f(x)) a  [#permalink]

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05 Aug 2017, 06:21
Ans A: a = -2
so F(x) = -2 ^@= 4
g(x) = x - 3--> 4-3 = 1 which is perfect sq
Re: f(x)=x^2 and g(x)=x−3. For which value of the following is g(f(x)) a   [#permalink] 05 Aug 2017, 06:21
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