If fx - x6 - 3x3 - 1- then find f 1-x in terms of fx-

f ( 1/x ) = (1/x #160; )^6 + 3 (1/x )^3 + 1 = 1 + 3x^3 + x^6/x^6 = f(x)/x^6 ...

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Definition of Functions

If fx = x6 ...

Question

If $f (x) = x^{6} + 3 x^{3} + 1$ , then find $f (\frac{1}{x})$ in terms of $f (x)$ .

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Solution

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f (x) = x^{6} + 3 x^{3} + 1

f (\frac{1}{x})

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If $f (x) = - \sqrt{25 - x^{2}}$ , then find ${lim}_{x \to 1} (\frac{f (x) - f (1)}{x - 1})$

f (x) = - \sqrt{25 - x^{2}}

lim x \to 1 \frac{f (x) - f (1)}{(x - 1)}

f (x) = \int_{1}^{x} \frac{l n t d t}{1 + t + t^{2}} (x > 0)

f (x) = - f (\frac{1}{x})

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

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