Do the mathematicians really know the exact values of what usually called “indeterminate forms”? @Todd Trimble well, I am interested in exact values rather than limits (the limits can only hint at exact values). Discrete math deals with exact values so I very much appreciate if someone knows the values of these expressions accepted and used in discrete math fields and the justifications.

how to solve f(f(x))=x^2+x If it were $f(f(x))=x^2+2x$ then the solution would be $f(x)=(1+x)^{\sqrt{2}}-1$ For your function the closed-form solution may be not existing.