- #1
jakncoke1
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Problem: Let S be the class of functions from $[0, \infty)$ to $[0, \infty)$ such that
1) $S_1 = e^{x} - 1, S_2 = ln(x + 1)$ are in S
2)if f(x), g(x) $\in S$, then f(x)+g(x), f(g(x)) are also in S
3)if f(x), g(x) $\in S$, and f(x) $\geq$ g(x) for $x \geq 0$, then f(x) - g(x) is in S
Prove that if f(x), g(x) $\in S$, then f(x)g(x) $\in S$.
1) $S_1 = e^{x} - 1, S_2 = ln(x + 1)$ are in S
2)if f(x), g(x) $\in S$, then f(x)+g(x), f(g(x)) are also in S
3)if f(x), g(x) $\in S$, and f(x) $\geq$ g(x) for $x \geq 0$, then f(x) - g(x) is in S
Prove that if f(x), g(x) $\in S$, then f(x)g(x) $\in S$.