Math Problem Statement
Which of the following functions is an even function?
Solution
To determine which of the given functions is an even function, we need to recall that a function is even if it satisfies the condition:
Let's evaluate each function:
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: This is not an even function.
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: This is an even function since .
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: This is not an even function.
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: This is not an even function.
Conclusion: The only even function among the given options is:
Would you like more details or have any further questions?
Related Questions:
- What defines an odd function?
- Can a function be both even and odd? If yes, give an example.
- How do trigonometric functions like and behave under the even-odd rule?
- What is the significance of symmetry in even functions?
- How do polynomial functions generally behave in terms of evenness or oddness?
- Can a non-polynomial function be even or odd?
- What are some practical applications of even and odd functions?
- How does the evenness of a function affect its graph?
Tip: Remember that even functions are symmetric with respect to the y-axis, which is a useful visual check when sketching graphs or solving problems.
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Math Problem Analysis
Mathematical Concepts
Functions
Even Function
Formulas
Definition of even function: f(-x) = f(x)
Theorems
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Suitable Grade Level
Grades 11-12