Relations and Functions
RS Aggarwal
CBSE
Grade 12
Question:
If $f: \mathbb{R} \to \mathbb{R}$ is given by $f(x) = (3 - x^3)^{1/3}$, then $(f \circ f)(x)$ is:
(a) $x$
(b) $x^3$
(c) $3 - x^3$
(d) $x^{1/3}$
Step-by-Step Solution
Key Concept: f(f(x)) = (3 - (3 - x^3))^{1/3} = (x^3)^{1/3} = x.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: $x$
Confused by the solution? Ask the AI to explain a specific step, tell you where you went wrong, or break down the key trap in this question.