On monotone boundedness of sequence function Let f (x) be monotonically bounded in (- ∞, + ∞) and {xn} be a sequence. The following proposition is correct () If a {xn} converges, then {f (xn)} converges B if {xn} is monotone, then {f (xn)} converges How to judge these two options?

On monotone boundedness of sequence function Let f (x) be monotonically bounded in (- ∞, + ∞) and {xn} be a sequence. The following proposition is correct () If a {xn} converges, then {f (xn)} converges B if {xn} is monotone, then {f (xn)} converges How to judge these two options?

Because {xn} is monotone, so is f (x)
F (xn) is monotone
F (x) is monotonically bounded in (- ∞, + ∞)
So f (xn) is monotonically bounded in (- ∞, + ∞)
According to the monotone boundedness theorem, we know that f (xn) must converge
That is convergence
Choose B