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

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It is given that

f(x) = |x|

We can write it as

f o f = f{f(x)} = f(|x|) = |x| …….. (1)

Same way

f = |x| …….. (2)

From both the equations we know that fof = f.

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