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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.
If f and g are both even functions, is f + g even?
We will use the concept of an even function to find whether f + g is an even function or not.
Answer: If f and g are even functions, then f + g is an even function.
Let us see how we will use the concept of even function to find whether f + g is an even function or not.
Explanation:
Let us consider a function h(x) = f(x) + g(x)
A function h(x) is an even function if h(-x) = h(x).
Since f and g are both even functions, so f(x) = f(-x) and g(x) = g(-x)
Substitute -x for x.
Now, h(-x) = f(-x) + g(-x) = f(x) + g(x) = h(x)
We see that h(x) = h(-x) .
Therefore, h(x) is also an even function.
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