If f : R R be given by f(x) = (3 - x 3 ) 1/3 , then fof (x) is (A) x 1/3 (B) x 3 (C) x (D) (3 - x 3 ) .

Option C is correct f:R R and f(x) = (3 - x 3 ) 1/3 f[f(x)] = [3 - f(x) 3 ] 1/3 f[f(x)] = [3 - (3 - x 3 ) 1/3 3 ] 1/3 = [3 - (3 - x 3 )] 1/3 = (3 - 3 + x 3 ) 1/3 = x

Relations and Functions — Class 12 Maths Solution

ncert exercise SA NCERT Ex. 1.3,Q.13, Page 19

Question

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

(A) ${x^{1/3}}$

(B) ${x^3}$

(D) $(3 - {x^3})$ .

Step-by-step Solution

Option C is correct

$f:R \to R$ and $f(x) = {(3 - {x^3})^{1/3}}$

$\Rightarrow$ $f[f(x)] = {[3 - {\{ f(x)\} ^3}]^{1/3}}$

$\Rightarrow$ $f[f(x)] = {[3 - {\{ {(3 - {x^3})^{1/3}}\} ^3}]^{1/3}}$

$= {[3 - (3 - {x^3})]^{1/3}} = {(3 - 3 + {x^3})^{1/3}} = x$

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