Question

For a monotonically increasing function f(x), is f(x3) also monotonically increasing?

a) Yes
b) No
c) Depends on the specific function
d) Only for even powers of x

Answer 1

The monotonicity of f(x^3) depends on the specific function and the domain of x. If x^3 is monotonically increasing over the domain of interest, then f(x^3) is also monotonically increasing. The answer isn't straightforward without additional details about f(x) and x's domain.

Step-by-step explanation:

For a monotonically increasing function f(x), whether f(x^3) is also monotonically increasing depends on the specific function and the domain of x. If the cube of x, that is x^3, is also monotonically increasing over the domain of interest, then f(x^3) is monotonically increasing as well. However, because x^3 is not monotonically increasing over the entire set of real numbers (since it decreases for negative values of x), we can only say that f(x^3) is monotonically increasing in scenarios where x is restricted to non-negative values or the function f has properties that make the composition monotonically increasing over its domain.