帮忙求这个函数的反函数
来源:学生作业帮 编辑:作业帮 分类:综合作业 时间:2024/05/25 04:55:27
帮忙求这个函数的反函数
两个大根号是3次根式
大根号内的两个小根号是开2次
对不起啊,图片看不了!网速太慢了!
再问: 式子是这样的 y = [ x + ( 1+x^2 )^(1/2) ]^(1/3) + [ x - ( 1+x^2 )^(1/2) ]^(1/3)
再答: 两边开三次方 y^3=2x+3(x+(1+x^2)^(1/2))^(1/3)*[ x - ( 1+x^2 )^(1/2) ]^(1/3)*{ [ x + ( 1+x^2 )^(1/2) ]^(1/3) + [ x - ( 1+x^2 )^(1/2) ]^(1/3)} 因为{}中等于y则 y^3=2x+3(x+(1+x^2)^(1/2))^(1/3)*[ x - ( 1+x^2 )^(1/2) ]^(1/3)*y 因为3(x+(1+x^2)^(1/2))^(1/3)*[ x - ( 1+x^2 )^(1/2) ]^(1/3)=-3 所以y^3=2x-3y x=(y^3+3y)/2 则y=(x^3+3y)/2
再问: 式子是这样的 y = [ x + ( 1+x^2 )^(1/2) ]^(1/3) + [ x - ( 1+x^2 )^(1/2) ]^(1/3)
再答: 两边开三次方 y^3=2x+3(x+(1+x^2)^(1/2))^(1/3)*[ x - ( 1+x^2 )^(1/2) ]^(1/3)*{ [ x + ( 1+x^2 )^(1/2) ]^(1/3) + [ x - ( 1+x^2 )^(1/2) ]^(1/3)} 因为{}中等于y则 y^3=2x+3(x+(1+x^2)^(1/2))^(1/3)*[ x - ( 1+x^2 )^(1/2) ]^(1/3)*y 因为3(x+(1+x^2)^(1/2))^(1/3)*[ x - ( 1+x^2 )^(1/2) ]^(1/3)=-3 所以y^3=2x-3y x=(y^3+3y)/2 则y=(x^3+3y)/2