Solving a transcendental equation using matlab

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How to solve x = sin(ax+b), when 'a' and 'b' takes all the real values in [0,1]? Can I use matlab to solve it?

I have understood to solve the equation when 'a' and 'b' both are fixed constants. But, I wish to know whether we have to find a solution for each pair of (a,b). If so, how to put them all together?

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Considering the function $f(x,y,z) = x-\sin(y x+z) = 0$ for $(-1\le x\le 1),( 0\le y\le 1), (0\le z\le 1)$ we can depict the following surface patch

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