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To plot solutions, FindRoot as a function


Hello,

I'd like to plot the solution of an equation which depends on two 
parameters, e.g.

a*Tanh[b*x] == x

So, I'd like to see it in 3D, one axis is "a", other is "b", and the last 
is "solution".

I've tried naively to do it as follows:

sol[a_,b_]:=FindRoot[a*Tanh[b*x] == x, {x, {0.01, 0.1}}]
Plot[sol[a,b], {a, 1, 2}, {b, 1, 2}]

And it doesn't work. Help me, please. What can I do?

Thanks a lot,

Veniamin





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