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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]  12 Jun 2017, 14:31
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84% (00:53) correct 15% (00:39) wrong based on 19 sessions

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

Indicate all such values:

❑ $$-2$$

❑ $$-1$$

❑ $$-\frac{1}{2}$$

❑ $$\frac{1}{2}$$

❑ 1

❑ 2
[Reveal] Spoiler: OA

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Joined: 03 Sep 2017
Posts: 521
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Kudos [?]: 343 [0], given: 66

Re: f(x) = x2 + 1. For which values of x does f(x) = [#permalink]  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]  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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