It is known that F & nbsp; (x) is an even function on R and increases monotonically on (0, + ∞), and F & nbsp; (x) < 0 holds for all x ∈ R. try to judge the monotonicity of − 1F (x) on (- ∞, 0) and prove your conclusion

It is known that F & nbsp; (x) is an even function on R and increases monotonically on (0, + ∞), and F & nbsp; (x) < 0 holds for all x ∈ R. try to judge the monotonicity of − 1F (x) on (- ∞, 0) and prove your conclusion

It is proved that − 1F (x) is a monotone decreasing function on (- ∞, 0). Let x1 ＜ x2 ＜ 0, then - x1 ＞ - x2 ＞ 0, ｜ f (- x1) ＞ f (- x2), ∵ f (x) is an even function, ｜ f (x1) ＞ f (x2) and − 1F (x) − [− 1F (x2)] = 1F (x2) − 1F (x1) = f (x1) − f (x2) f (x1) > 0 (

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