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CBSE Class 12 · 2006 · Relations And Functions XIIVery Short Answer

If

f : R \to R

is given by

f (x) = (3 - x^{3})^{1/3}

, then find the value of

f o f (x)

.

Answer: $f o f (x) = x$

Solution

We substitute

f (x)

into

f

itself, because

f o f (x) = f (f (x))

.

f o f (x) = f ((3 - x^{3})^{1/3}) = (3 - [(3 - x^{3})^{1/3}]^{3})^{1/3}

The inner cube undoes the cube-root, so the bracket collapses cleanly.

= (3 - (3 - x^{3}))^{1/3} = (x^{3})^{1/3} = x

f o f (x) = x

CBSE Class 12 Board · 2006 · Subjective

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