Question

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

(A) 1 / x^3
(B) x^3
(C) x
(D) (3 − x^3 )

Answer 1

$\bold{Answer :}$

Given that,

f (x) = (3 - x³)^(1/3)

Now, fof (x)

= f (f (x))

= f {(3 - x³)^(1/3)}

= [3 - {(3 - x³)^(1/3)}^3]^(1/3)

= {3 - (3 - x³)}^(1/3)

= (3 - 3 + x³)^(1/3)

= (x³)^(1/3)

= x

Therefore, option (C) is correct.

#$\bold{MarkAsBrainliest}$

Answer 2

$f:\mathbb{R}\rightarrow\mathbb{R}$ given by $\bf{f(x)=\sqrt[3]{3-x^3}}$

we have to find out fof(x)
fof(x) = f(f(x))
$=f(\sqrt[3]{3-x^3})\\=\sqrt[3]{3-(\sqrt[3]{3-x^3})^3}\\=\sqrt[3]{3-3+x^3}=\sqrt[3]{x^3}=x$
hence, option (C) is correct .