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f(x) = x2 + 1. For which values of x does f(x) =

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f(x) = x2 + 1. For which values of x does f(x) = [#permalink] New post 12 Jun 2017, 14:31
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\(f(x) = x^2 + 1\). For which values of x does \(f(x) = f (\frac{1}{x})\)?

Indicate all such values:

❑ -2

❑ -1

❑ \(\frac{-1}{2}\)

❑ 1/2

❑ 1

❑ 2

[Reveal] Spoiler: OA
B and E
[Reveal] Spoiler: OA

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Re: f(x) = x2 + 1. For which values of x does f(x) = [#permalink] New post 24 Sep 2017, 08:47
It is quite straightforward to notice that the only value of x that are equal when considered as 1/x are -1 and +1. Since in the formula for f(x) the x is squared and then summed to 1, it is easy to see that every other solution would have lead to two different values when considering x and 1/x.

Answers B and E!
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Re: f(x) = x2 + 1. For which values of x does f(x) = [#permalink] New post 24 Sep 2017, 12:11
Carcass wrote:


\(f(x) = x^2 + 1\). For which values of x does \(f(x) = f (\frac{1}{x})\)?

Indicate all such values:

❑ -2

❑ -1

❑ \(\frac{-1}{2}\)

❑ 1/2

❑ 1

❑ 2

[Reveal] Spoiler: OA
B and E


We have \(f(x) = f (\frac{1}{x})\) and given f(x) =\(x^2\)+1

now substituting we get -

\(x^2\)+1 = \((\frac{1}{x})^2\) +1

or \(x^2\)+1 = \(\frac{1+x^2}{x^2}\)

or cross multiflication

\(x^4\)+\(x^2\) = 1+ \(x^2\)

or \(x^4\) =1

Only -1 and 1 fits the equation
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Re: f(x) = x2 + 1. For which values of x does f(x) =   [#permalink] 24 Sep 2017, 12:11
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f(x) = x2 + 1. For which values of x does f(x) =

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