Question: For each real function f, define the positive part of f by and the negative part of / by a) Prove that f+(x) > 0,

For each real function f, define the positive part of f by
For each real function f, define the positive part of

and the negative part of / by

For each real function f, define the positive part of

a) Prove that f+(x) > 0, f-(x) > 0, f(x) = f+(x) - f-(x% and |f(x)| = f+(x) + f-(x) all hold for every x ˆŠ Dom (f).
b) Prove that if

For each real function f, define the positive part of

exists, then f+{x) †’ L+ and f-(x) †’ L- as x †’ a.

(x)1 + f(x) x e Dom (f.) f+ (x) = , r e Dom( lim f(x)

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