Calculate $f (2)$ $f(2)$ , knowing that with any $x \neq 0$ $x≠0$ the correct equality $f (x) + 3 f (1 x) = x^{2}$ $f(x)+3f(1x)=x^2$ ??

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Calculate $f (2)$ $f(2)$ , knowing that with any $x \neq 0$ $x≠0$ the correct equality $f (x) + 3 f (1 x) = x^{2}$ $f(x)+3f(1x)=x^2$ ??

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Answer 1 · 2017-10-01T17:52:44

The answer is $f (2) = 1$ $f(2)=1$ .

Explanation:

First and foremost, it is imperative to note that $f (1 x) = f (x)$ $f(1x)=f(x)$ . With this in mind, $f (x) + 3 f (x) = x^{2}$ $f(x)+3f(x)=x^2$ can be simplified as follows:
$f (x) + 3 f (x) = x^{2}$ $f(x)+3f(x)=x^2$
$4 f (x) = x^{2}$ $4f(x)=x^2$
$f (x) = \frac{x^{2}}{4}$ $f(x)=(x^2)/4$

From here, substitute 2 wherever you have x:
$f (2) = \frac{{(2)}^{2}}{4} = 1$ $f(2)=(2)^2/4=1$ .

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Calculate $f (2)$ $f(2)$ , knowing that with any $x \neq 0$ $x≠0$ the correct equality $f (x) + 3 f (1 x) = x^{2}$ $f(x)+3f(1x)=x^2$ ??

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Explanation:

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Calculate f(2)f(2)f(2), knowing that with any x≠0x≠0x≠0 the correct equality f(x)+3f(1x)=x^2f(x)+3f(1x)=x2f(x)+3f(1x)=x^2 ??

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Explanation:

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Calculate $f (2)$ $f(2)$ , knowing that with any $x \neq 0$ $x≠0$ the correct equality $f (x) + 3 f (1 x) = x^{2}$ $f(x)+3f(1x)=x^2$ ??