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For real values:
$1 - x^2 - y^2 \ge 0$
$x^2 + y^2 \le 1$
Minimum value of $\sqrt{1 - x^2 - y^2}$ is $0$ (when $x^2+y^2=1$)
Maximum value is $1$ (when $x=y=0$)
So exponent varies from $0$ to $1$
$e^0 = 1$
$e^1 = e$
Hence range is $[1, e]$
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