Question

If $f\left(x\right)=(a-x^n{)}^{\frac{1}{n}}$ where a > 0 and n is a positive integer, then $f\left[f\right(x\left)\right]$

• A. x
• B. -x
• C. f(x)
• D. -f(x)

Answer 1

The correct option is A x

Hence (A) is the correct answer
$f\left(x\right)=(a-x^n{)}^{\frac{1}{n}}$, a > 0,n in +ve integer
$f\left(f\right(x\left)\right)=f\left[\right(a-x^n{)}^{\frac{1}{n}}]={[a-{\left\{\right(a-x^n{)}^{\frac{1}{n}}\}}^n]}^{\frac{1}{n}}=(a-a+x^n{)}^{\frac{1}{n}}=x$