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试用两种方法求函数f(x)=x^2/(x^2+1)的值域.
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1:x不等于0时,由题意f(x)=x^2/(x^2+1)=1/(1+1/x^2),x^2取值范围是(0,正无穷),所以1+1/x^2取值范围是(1,正无穷),所以f(x)=x^2/(x^2+1)=1/(1+1/x^2)取值范围是(0,1);x等于0时,f(0)=0;综上,f(x)=x^2/(x^2+1)取值范围是【0,1)
2:由题意f(x)=x^2/(x^2+1)=1-1/(x^2+1),x不等于0时,1+x^2取值范围是(1,正无穷),所以f(x)=x^2/(x^2+1)=1-1/(x^2+1)取值范围是(0,1);x等于0时,f(x)=x^2/(x^2+1)=f(0)=0,综上,f(x)=x^2/(x^2+1)取值范围是【0,1)
2:由题意f(x)=x^2/(x^2+1)=1-1/(x^2+1),x不等于0时,1+x^2取值范围是(1,正无穷),所以f(x)=x^2/(x^2+1)=1-1/(x^2+1)取值范围是(0,1);x等于0时,f(x)=x^2/(x^2+1)=f(0)=0,综上,f(x)=x^2/(x^2+1)取值范围是【0,1)
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