Assume that f is an even function, g is an odd function, and both f and g are defined on the entire real line. State whether
the combination of functions (where defined) is even or odd.
-$$\mathrm { g } ^ { 2 }$$
A) Even
B) Odd

Question

Quizplus · Accepted Answer

The square of an odd function is an even function because squaring the function negates the effect of input sign change (i.e., $(g(-x))^2 = (g(x))^2$), thus satisfying the definition of an even function.

Assume That F Is an Even Function, G Is an Odd