1.

If f : R → R such that f(x) : (3 - x3)1/3 then prove that (fof) (x) = x.

Answer»

Given, f(x) = (3 - x3)1/3

L.H.S. = fof(x)

= f[f(x)]

= f{(3 - x3)1/3}

= 3 - {(3 - x3)1/3}1/3

= [3 - 3 + x3]1/3 = (x3)1/3

= x



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