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# If f(x) = x^2 + 1 and g(x) = x^2 – 1, what is the value of g(f(x))?

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If f(x) = x^2 + 1 and g(x) = x^2 – 1, what is the value of g(f(x))?  [#permalink]

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17 Apr 2018, 01:19
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If $$f(x) = x^2 + 1$$ and $$g(x) = x^2 – 1$$, what is the value of $$g(f(x))$$?

A. $$x^2$$

B. $$x^4 – 1$$

C. $$x^4 + 2x^2$$

D. $$x^2 + 2x$$

E. $$x^4 + 2x^2 + 2$$

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Re: If f(x) = x^2 + 1 and g(x) = x^2 – 1, what is the value of g(f(x))?  [#permalink]

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17 Apr 2018, 02:26
Bunuel wrote:
If $$f(x) = x^2 + 1$$ and $$g(x) = x^2 – 1$$, what is the value of $$g(f(x))$$?

A. $$x^2$$

B. $$x^4 – 1$$

C. $$x^4 + 2x^2$$

D. $$x^2 + 2x$$

E. $$x^4 + 2x^2 + 2$$

Given:
$$f(x) = x^2 + 1$$
$$g(x) = x^2 – 1$$

Therefore, g(f(x)) = g(x^2 + 1) = $$(x^2 + 1)^2 - 1 = x^4 + 2x^2 + 1 - 1 = x^4 + 2x^2$$ (Option C)

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Re: If f(x) = x^2 + 1 and g(x) = x^2 – 1, what is the value of g(f(x))?  [#permalink]

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17 Apr 2018, 04:10
Option C, this is a simple substitution question where we need to submit f(x) in the x of g(x).
where g(f(x)) = f(x)^2-1 = (x^2+1)^2-1 = x^4+2*x^2+1-1 = x^4+2*x^2 Option C
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Re: If f(x) = x^2 + 1 and g(x) = x^2 – 1, what is the value of g(f(x))?  [#permalink]

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18 Apr 2018, 11:28
g(f(x))=(x^2+1)^2-1=(x^4+2x^2+1)-1=x^4+2x^2(Ans C)
Re: If f(x) = x^2 + 1 and g(x) = x^2 – 1, what is the value of g(f(x))?   [#permalink] 18 Apr 2018, 11:28
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