Find the sum and product of identity function and the modulus function.

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Solution

identity function is $f (x) = x$ , modulus function is $f (x) = | x |$

sum of them $= x + | x |$

that is equal to
$2 x$ if $x > 0$ and $0$ if $x < 0$

product of them is $x \times | x |$

that is equal to $x^{2}$ if $x > 0$ and $- x^{2}$ if $x < 0$

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