In[]:=
FunctionRange[y^2/4+Sqrt[(x-y^2/4)^2+(E^x-y)^2]+1,{x,y},z,Reals,Method{"Reduced"True}]
FunctionRange
:Unable to find the exact range. Returning bounds on the range computed using numeric optimization methods.
Out[]=
1.41421≤z≤1.998×
13
10
In[]:=
FunctionRange[y^2/4+Sqrt[(x-y^2/4)^2+(E^x-y)^2]+1,{x,y},z,Reals,WorkingPrecisionMachinePrecision]
Out[]=
z≥1.41421
In[]:=
FunctionRange[y^2/4+Sqrt[(x-y^2/4)^2+(E^x-y)^2]+1,{x,y},z,Reals,Method{"Reduced"True},WorkingPrecisionMachinePrecision]
Out[]=
1.41421≤z≤1.998×
13
10
In[]:=
NMinimize[{y^2/4+Sqrt[(x-y^2/4)^2+(E^x-y)^2]+1,{x,y}∈Reals},{x,y}]
Out[]=
{1.41421,{x-5.11793×
-13
10
,y0.828427}}