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.
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
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