Question

If f : R→R be given by f(x)= \((3-x^3)^\frac {1} {3}\),,then fof(x) is 

• A. \(\frac {1} {x^3}\)
• B. \(x^3\)
• C. X
• D. \((3-x^3)\)

Answer 1

The Correct Option is C

f: R → R is given as f(x)= \((3-x^3)^\frac {1} {3}\).
Therefore fof (x)= f ( f (x) )=\(f \Bigg (3-x^3)^\frac {1} {3} \Bigg )\)= \(\Bigg [ 3 - \bigg ( ( 3 - x^3) ^ \frac {1} {3} \bigg )^3 \Bigg ]^ \frac {1} {3}\)
= \([ 3 - (3 - x^3 ) ]^ \frac {1} {3} = (x^3)^ \frac {1} {3} = x\)
∴ fof (x)= x