令t=根号下1-x^2,则t^2=1-x^2,x^2=1-t^2
y=-t^2+t+1=-(t-1/2)^2+5/4
因为1-x^2≤1,所以0≤根号下1-x^2≤1,0≤t≤1
所以-1/2≤t-1/2≤1/2,0≤(t-1/2)^2≤1/4
所以1≤-(t-1/2)^2+5/4≤5/4,1≤t≤5/4
所以y=X^2+根号下1-x^2的值域是[1,5/4]