S = {x∈ R^n :1 < x ≤ 2}} ,证明或反证：“存在一个连续方程

S = {x∈ R^n :1 < x ≤ 2}} ,证明或反证：“存在一个连续方程
f :R^n → R使得对于所有x∈ R^n S,每当x∈ S 且 f (x) ≤ 2时,f (x) > 2
英文是 Let S = {x∈ Rn :1 < x ≤ 2}} .Prove or disprove the statement:
“There exists a continuous function f :Rn → R such that f (x) > 2 whenever
x∈ S and f (x) ≤ 2 for all x∈ Rn S .”