If f(x)=f(-x), then it is ______ function.
Question
If f(x)=f(-x), then it is ______ function.
Solution 1
The function is an even function.
Here's why:
A function f(x) is said to be an even function if for every x in the function's domain, f(x) = f(-x). This means that the function is symmetric about the y-axis. The graph of an even function can be folded along the y-axis and both halves would match exactly.
So, if f(x) = f(-x), then the function is an even function.
Solution 2
The function is an even function.
Here's why:
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A function f(x) is said to be an even function if for every x in the function's domain, f(x) = f(-x). This is the definition of an even function.
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In the given question, it is stated that f(x) = f(-x).
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Therefore, based on the definition of an even function, the function in the question is an even function.
Solution 3
The function is an even function.
Here's why:
A function f(x) is said to be an even function if for every x in the function's domain, f(x) = f(-x). This means that the function is symmetric about the y-axis. The graph of an even function can be folded along the y-axis and both halves would match exactly.
So, if f(x) = f(-x), then the function is an even function.
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