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FindRoot question

I have a question concerning efficient use of FindRoot.

Consider the following code:




j2[t_,b_]:= -(2*h*k - 4*b*h*k + b*h^2*k + 2*b*h*k^2 - 4*f*t + 4*b*f*t - 2*b*f*k*t +  b*h*k*t)/(2*(2 - 2*b + b*k)*(-h + t))   

j3[t_,b_]:=N[Which [j2[t,b]<0,0,j2[t,b]>1,1,True,j2[t,b]]]

j4[z_]:=N[Integrate[b j3[z,b],{b,0,1}]]

This works fine.  j2 defines a function, j3 truncates it at 0 and 1,
and j4 integrates j3 with respect to one of its arguments.  Nothing
complicated here.

If I do:

Plot [z j4[z]-f,{z,0,1}]

I get a nice upward sloping graph that clearly crosses the horizontal
axis at about z=.4.  So, z=.4 is approximately a real root.

Next, I try:

FindRoot [z j4[z]-f,{z,.4}]

But (and this is the problem) mathematica just sits there.  I presume
it is calculating, but I have been waiting for over 15 minutes and it
is still grinding away, this despite the fact that my guess at the
root (.4) is alomost correct.  Am I doing something wrong?  Is there
an easier way to get mathematica to calculate roots?



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