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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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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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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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New post 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.

Answer: A
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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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New post 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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New post 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

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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] 05 Aug 2017, 06:21
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