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# The function f is defined for all real numbers x as f(x)=x2−1. What is

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Joined: 02 Sep 2009
Posts: 51185
The function f is defined for all real numbers x as f(x)=x2−1. What is  [#permalink]

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09 Apr 2018, 01:01
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Difficulty:

5% (low)

Question Stats:

97% (00:35) correct 3% (00:56) wrong based on 87 sessions

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The function f is defined for all real numbers x as f(x) = x^2 − 1. What is f(f(3))?

A. 26
B. 47
C. 63
D. 75
E. 80

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Re: The function f is defined for all real numbers x as f(x)=x2−1. What is  [#permalink]

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09 Apr 2018, 01:52
1
f(3) = 3^2 - 1 = 8

f(f(3) = f(8) = 8^2 - 1 = 63

Option C.

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Re: The function f is defined for all real numbers x as f(x)=x2−1. What is  [#permalink]

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09 Apr 2018, 03:48
Bunuel wrote:
The function f is defined for all real numbers x as f(x) = x^2 − 1. What is f(f(3))?

A. 26
B. 47
C. 63
D. 75
E. 80

Given: f(x) = $$x^2 - 1$$

f(f(x)) = f($$x^2 - 1$$) = $$(x^2 - 1)^2 - 1 = x^4 - 2x^2 + 1 - 1 = x^4 - 2x^2$$

Therefore, $$f(f(3)) = 3^4 - 2*3^2 = 81 - 18$$ = 63(Option C)
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Re: The function f is defined for all real numbers x as f(x)=x2−1. What is  [#permalink]

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09 Apr 2018, 05:10
We can break x^2-1 =[x+1][x-1]
So f(3)= 4x2=8

And F(f(3))=f(8) = (8+1) (8-1) = 63

Option C :63

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Re: The function f is defined for all real numbers x as f(x)=x2−1. What is  [#permalink]

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10 Apr 2018, 16:09
Bunuel wrote:
The function f is defined for all real numbers x as f(x) = x^2 − 1. What is f(f(3))?

A. 26
B. 47
C. 63
D. 75
E. 80

f(3) = 3^2 - 1 = 8

f(f(3)) = f(8) = 8^2 - 1 = 63

So f(f(3)) = 63.

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Re: The function f is defined for all real numbers x as f(x)=x2−1. What is &nbs [#permalink] 10 Apr 2018, 16:09
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