\(\sqrt2 -1\approx 0.4 \Rightarrow \sqrt2 -1 \in (0,1)\)
\(|x|\) is always non-negative, so the range of \((\sqrt2-1)^{|x|}\) is \((0,1]\)
The range of \(\sin x\) is \([-1,1]\) => the range of \(\sin^2x\) is \([0,1]\) => the range of \(\sin^2x+1\) is \([1,2]\)
The only common point of these two function is the one with y-coordinate = 1, so \(y=1\). Let's take one of these functions and find for which x, its value is equal to 1. I'll take the first one.
\((\sqrt2-1)^{|x|}=1\\
\Downarrow\\
|x|=0\\
x=0\)
So, \(x=0\) :)
