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Question

Mathematics Question on Relations and Functions

If f :****R→R be given by f(x) = (3−x3)13(3-x^3)^\frac {1} {3},,then fof(x) is

A

1x3\frac {1} {x^3}

B

x3x^3

C

X

D

(3−x3)(3-x^3)

Answer

X

Explanation

Solution

f:R → R is given as f(x) = (3−x3)13(3-x^3)^\frac {1} {3}.
Therefore fof (x) = f ( f (x) ) =f(3−x3)13)f \Bigg (3-x^3)^\frac {1} {3} \Bigg )= [3−((3−x3)13)3]13\Bigg [ 3 - \bigg ( ( 3 - x^3) ^ \frac {1} {3} \bigg )^3 \Bigg ]^ \frac {1} {3}
= [3−(3−x3)]13=(x3)13=x[ 3 - (3 - x^3 ) ]^ \frac {1} {3} = (x^3)^ \frac {1} {3} = x
∴ fof (x)= x