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JEE MATHEMATICS MCQ: FUNCTIONS

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Two functions ff and gg are said to commute, if (f∘g)(x)=(g∘f)(x),∀x(f \circ g)(x)=(g \circ f)(x), \forall x, then which one of the following functions are commute?
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Correct option: C
f(x)=xm,g(x)=xn,m≠n,m,n∈If(x)=x^m, g(x)=x^n, m \neq n, m, n \in I \quad ( II is the set of all integers)
Based on the provided information, the simplified form of f(x)=∣x−2∣+∣2−x∣,−3≤x≤3f(x)=|x-2|+|2-x|,-3 \leq x \leq 3 is {2x,2≤x≤34,−2≤x<2−2x,−3≤x<−2\left\{\begin{array}{cc}2 x, & 2 \leq x \leq 3 \\ 4, & -2 \leq x<2 \\ -2 x, & -3 \leq x<-2\end{array}\right., which is option A.

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