Question

T/F explain why if its true or false.

if g is an even function and h = f o g than h is also an even function

Answer 1

True

Let h be the composition f∘g

Then by the definition of even function, h is an even function if:

h (− x) = h (x)

Since g is specified as an even function, you have that:

g (− x) = g (x) for all x

Therefore, since one property of a function is that x = y => f (x) = f(y)

By substitution you have f (g (− x ) = f (g(x)) for all x

Written in terms of the composition h, this is the statement that h (−x) = h (x)

So h is an even function.