if `f(x)=(a-x^n)^(1/n),` where `a > 0 and n` is a positive integer, then `f(f(x))=` (i) `x^3` (ii) `x^2` (iii) `x` (iv) `-x`

Question

if `f(x)=(a-x^n)^(1/n),` where `a > 0 and n` is a positive integer, then `f(f(x))=` (i) `x^3` (ii) `x^2` (iii) `x` (iv) `-x`

Answer 1

Correct Answer - 1
Given, `f(x)=(a-x^(n))^(1//n)`
`rArr f[f(x)]=[a-{(a-x^(n))^(1//n)}^(n)]^(1//n)=(x^(n))^(1//n)=x`
` therefore f[f(x)]=x`
Hence, given statement is true.