# FunctionRange giving "false"

I was trying to find the range of a function I obtained in some context. The code is as follows

FunctionRange[{1/2 (1 - Sqrt[-1 + 4 Abs[x]] Sqrt[-1 + 4 Abs[z]]), 0 < Abs[x] < 1/4 && 0 < Abs[z] < 1/4}, {Abs[x], Abs[z]}, y]

The above code when executed gives False. What is the meaning of false and how to find the range of function in this case?

What is the meaning of false and how to find the range of function in this case?

The default for domain is Reals

When it returns False it means there is no range in the reals.

FunctionRange[{1/2 (1 - Sqrt[-1 + 4 Abs[x]] Sqrt[-1 + 4 Abs[z]]),
0 < Abs[x] < 1/4 && 0 < Abs[z] < 1/4}, {Abs[x],
Abs[z]}, y]

(*False*)


Change to complex

FunctionRange[{1/2 (1 - Sqrt[-1 + 4 Abs[x]] Sqrt[-1 + 4 Abs[z]]),
0 < Abs[x] < 1/4 && 0 < Abs[z] < 1/4}, {Abs[x],
Abs[z]}, y, Complexes]


• Thanks. And there are situations when it returns "True" then does it means that all the reals are in the range? Jul 24, 2020 at 11:18
• @tanaypathak that is correct. For example FunctionRange[y, x, y] returns trues, means from -Infinity to +Infinity Jul 24, 2020 at 14:01