Question

f(x)=((x/3)^(2/3)±sqrt((x/3)^(4/3)-4*(x/3)^2+4))/(2/3) 的图像是什

Answer 1

(x/3)^(4/3)-4*(x/3)^2+4=((x/3)^2-2)^2

所以f(x)=((x/3)^(2/3)±((x/3)^2-2))/(2/3)=(2(x/3)^(2/3)-2)/(2/3)=3(x/3)^(2/3)-3=3^1/3*x^2/3-3

图像是单调递增向下弯曲的曲线,与y轴负半轴有交点