Question

The algebraic independence of some functions delimits some categories of functions. Knowing how to recognize when a function is algebraic or not helps in some mathematical manipulations, such as derivation. In view of the knowledge about algebraic functions, analyze the following statements:

I. Algebraic functions are those defined only by basic algebra operations.

II. There are explicit non-algebraic functions.

III. The transcendent functions are algebraic functions.

IV. f (x) = ln (x) is not an algebraic function.

Only what is stated in:

1. II, III e IV.

2. I, II e IV.

3. II e III.

4. I, III e IV.

5. I e IV.

Answer 1

The answer is option (b).