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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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New post 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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New post 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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New post 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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New post 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)
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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))? &nbs [#permalink] 18 Apr 2018, 11:28
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