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  4. If 3f(x) - f((1/x)) = log x4, then f(e-x) is

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Q. If $3f\left(x\right) - f\left(\frac{1}{x}\right) = log\,x^{4}$, then $f\left(e^{-x}\right)$ is

Relations and Functions

Solution:

$3f\left(x\right) - f\left(\frac{1}{x}\right) = log\,x^{4};\quad x \equiv \frac{1}{x}$
$3f\left(\frac{1}{x}\right) - f \left(x\right) = log \left(\frac{1}{x}\right)^{4}$
After solving we get $f\left(x\right) = log\, x$
$f\left(e^{-x}\right) = log_{e} e^{-x} = -x$