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1) Find functions f and g and sets S and T such that f(f −1 (T))...

1) Find functions f and g and sets S and T such that f(f −1 (T)) 6= T and g −1 (g(S)) 6= S.

2) Show that |ab| = |a||b| for any real numbers a, b.

3) Show that |a − b| ≥ ||a| − |b|| for any real numbers a, b.

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