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A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
Suppose g is an even function and let h = f.g. Is h always an even function?
Solution:
A function is even if f(x) = f(−x) for all x.
This means that the function is the same for +ve x-axis and ,-ve x-axis, or graphically, symmetric about the y-axis.
Given:
g is an even function and h = f.g
The even function is defined as function that even if we replace ‘x’ with ‘-x’ we get the same function
Let us consider an example of g being an even function
Let g = x2 and h = f(g(x))
⇒ h = f(x2)
f(x2) will always be positive irrespective of type of function as we have x2 in it which always gives a positive value.
Hence,
if g is an even function and h = f.g then h will always be even function
Suppose g is an even function and let h = f.g. Is h always an even function?
Summary:
If g is an even function and h = f.g then h always an even function.
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