Chapter 1 - Precalculus Review - 1.3 The Basic Classes of Functions - Exercises - Page 23: 22

Algebraic

According to the book, an algebraic function is made by "taking sums, products, and nth roots of polynomials and rational functions". We see that $ f(x)$ has the term $\sqrt{x}$ in the denominator, so it is not rational (ratio of polynomials), but rather algebraic.