If $f(x)=\left(3-x^7\right)^{\frac{1}{7}} ~\forall ~x \in R$, then $f(f(x))=$
Answer & explanation
Correct answer: option 1
$f(x)=\left(3-x^7\right)^{1 / 7}$
$f(f(x))=\left(3-f(x)^7\right)^{\frac{1}{7}}=\left(3-\left(\left(3-x^7\right)^{1 / 7}\right)^7\right)^{\frac{1}{7}}=x$
Hence (1) is the correct answer.