设f(x)是零到正无穷上的连续函数,且f(x)=f(x^2),x属于零到正无穷,证...答:证明:设 x = y^2,f(y)=f(y^2), ===> f(x)= f(x^(1/2))任给x 大于0, 不等于1, f(x) = f(x^(1/2))= f(x^(1/4))=...=f(x^(1/2^n))=...因为 x, x^(1/2), ..., x^(1/2^n), ... ---> 1 根据连续性, 于是 f(1)=lim f(x^(...
设函数f(x)=e^x-x (1) 求函数f(x)的单调区间 (2) 证明 当x属于R时...答:(1)f(x)=e^x-x,f′(x)=e^x-1,由f′(x)=e^x-1>0得x>0,所以单调增区间为(0,+∞),由f′(x)=e^x-1<0得x<0,所以单调减区间为(-∞,0);(2)设g(x)=e^x-x-1,则g′(x)=e^x-1,由g′(x)=e^x-1>0得x>0,所以单调增区间为(0,+∞),由g′(x)=e^x-1<0得...