In this question, the answer says that $f \circ g(x) = x$. But I am unable to get this result. The expression I am able to get is that $$f \circ g(x) = 7(x\text{ mod } 3) + 57(x\text{ mod }7) \pmod {21}.$$ I am unable to proceed any further.
2026-03-30 02:03:34.1774836214
Simplify functions involving modular arithmetic
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Let $x \mod 3 = a$ and $x \mod 7 = b$. Thus $a = x + 3 y$ and $b = x + 7 z$ for some integers $y$ and $z$. Express $7 a + 57 b$ in terms of $y$ and $z$. What do you get mod $21$?