State whether the composite function f(g(x)) is an odd function, an even function, or neither in the following situations.

Question

a. F and g are odd functions.

b. F and g are even function.

c. F is odd, and g is even.

d. F is even, and g is odd. 

Answer 1

a)  Let  f and g be odd functions.

 

f(g(x)) = f(g(-x)) = f(-g(x)) = - f(g(x)) so the composition in this case is also odd.

 

An example is f(x) = x,  g(x) = x³.