Question

Does the inverse of f(x) = {2 + (x − 3)³}^1/3 exist? If so, find it.

Answer 1

We have

f(x) = {2 + (x − 3)³}^1/3

Since 2 + (x − 3)³ is a polynomial function, it is continuous. Its domain and range both equal to R. Hence, it is onto (surjective). Thus, f(x) being a positive rational power of the continuous function is also continuous.

except at x = 3 and x = 3 − 21/3. Therefore, f(x) is monotonically strictly increasing and so invertible. Let