Let f : R → R : f(x) = |x|, prove that f o f = f.

Question

Philoid · Accepted Answer

To prove: f o f = f

Formula used: f o f = f(f(x))

Given: (i) f : R → R : f(x) = |x|

Solution: We have,

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

Clearly f o f = f.

Hence Proved.