Show F(x) is even
To show that a function F(x) is even, we need to prove that F(x) = F(-x) for all values of x
To show that a function F(x) is even, we need to prove that F(x) = F(-x) for all values of x.
Let’s start by considering the function F(x). Since we are trying to prove that F(x) is even, we can write F(x) = F(-x).
By assuming F(x) = F(-x), we need to examine and compare the two expressions in order to determine if they are equal for all values of x.
Now, let’s analyze the left-hand side of the equation, F(-x). This means we substitute -x for x in the function F(x). So, F(-x) = F(-(-x)), which simplifies to F(-x) = F(x).
As we can see, the expression F(-x) is equal to the expression F(x) for all values of x. Therefore, our assumption holds true and we have proven that F(x) is even, as F(x) = F(-x).
To summarize, a function F(x) is considered even if it satisfies the property F(x) = F(-x) for all values of x. In this proof, we showed that F(-x) is equal to F(x), which confirms that F(x) is indeed even.
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