Question

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

• A. $1+x$
• B. $1/x$
• C. $x$
• D. $-x$

Answer 1

Answer: (D)

$3f\left(x\right)-f\left(\frac{1}{x}\right)=log{x}^4;x\equiv \frac{1}{x}$
$3f\left(\frac{1}{x}\right)-f\left(x\right)=log{\left(\frac{1}{x}\right)}^4$
After solving we get $f\left(x\right)=logx$
$f\left(e^{-x}\right)=lo{g}_e{e}^{-x}=-x$