Are we missing some information?
What does a=0 and b=1 have to do with the solution? My guess: a <= x <= b?
Why do you require an IF formula? Are you supposed to use Iterative calculation? LAMBDA?
There are 3 solutions. See the image below.
I used Solver to find the solutions in A3 and A4. I wrote my own function to find the solution in A2. (PS: But Goal Seek finds a close solution.)
The formula for f(x) in B2 is:
=A2^3 - 3*A2 + 1
The values of x are:
A2: -1.87938524157182
A3: 0.347296355333864
A4: 1.53208888623792
