"if" function for math equations

oksanasana 

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

oksanasana 

You may use Goal Seek (Data->What-If-Analysis) for that