※ 引述《dondonmike (我很單純)》之銘言：
: Let V be the real vector space of all function f from R to R
: prove or disprove following sets of functions are subspace of V
: 1. all f such that f(x^2)=f(x)^2
no
(f+g)(x^2)=f(x^2)+g(x^2)=f(x)^2+g(x)^2
(f+g)(x)^2=f(x)^2+2fg(x)+g(x)^2
: 2. all f such that f(0)=1
no
0函數不在裡面
: 3. all f such that f(0)=1+f(1)
no
同上
: 4. all f which are continues
yes
0函數是連續函數
連續函數相加或乘以常數倍還是連續函數
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