Is there a continuous function f R R such that for every re

Is there a continuous function f : R R such that for every real y there are precisely three solutions to the
equation f(x) = y?

Solution

We know that,

A cubic polynomial has precisely three solutions.

It may have one real solution and two imaginary solution or all the solution may be real.

So,

y = x³ has precisely three solutions.

For any real value of y we get either all solution as real or two imaginary solution and one real solution.