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If f(x) is an even function, where f(x) ≠ 0, then which one of the following is correct?
- a)f′ (x) is even function
- b)f′ (x) is odd function
- c)f′ (x) may be an even or odd function depending on the type of function
- d)f′ (x) is a constant function
Correct answer is option 'B'. Can you explain this answer?
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If f(x) is an even function, where f(x) ≠ 0, then which one of the ...
f(x) is even function ⟹ f ′ (x) is odd function.
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If f(x) is an even function, where f(x) ≠ 0, then which one of the ...
If f(x) is an even function, it means that the function is symmetrical with respect to the y-axis. In other words, if we reflect the graph of f(x) across the y-axis, it will look exactly the same.
Mathematically, this can be expressed as f(x) = f(-x) for all x in the domain of the function.
For example, if f(x) = x^2, then f(-x) = (-x)^2 = x^2, which is equal to f(x). So, f(x) = x^2 is an even function.
Similarly, if f(x) = cos(x), then f(-x) = cos(-x) = cos(x), which is equal to f(x). So, f(x) = cos(x) is an even function.
Even functions can have various properties and characteristics, but the key defining feature is their symmetry about the y-axis.
Mathematically, this can be expressed as f(x) = f(-x) for all x in the domain of the function.
For example, if f(x) = x^2, then f(-x) = (-x)^2 = x^2, which is equal to f(x). So, f(x) = x^2 is an even function.
Similarly, if f(x) = cos(x), then f(-x) = cos(-x) = cos(x), which is equal to f(x). So, f(x) = cos(x) is an even function.
Even functions can have various properties and characteristics, but the key defining feature is their symmetry about the y-axis.
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If f(x) is an even function, where f(x) ≠ 0, then which one of the following is correct?a)f′ (x) is even functionb)f′ (x) is odd functionc)f′ (x) may be an even or odd function depending on the type of functiond)f′ (x) is a constant functionCorrect answer is option 'B'. Can you explain this answer?
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If f(x) is an even function, where f(x) ≠ 0, then which one of the following is correct?a)f′ (x) is even functionb)f′ (x) is odd functionc)f′ (x) may be an even or odd function depending on the type of functiond)f′ (x) is a constant functionCorrect answer is option 'B'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about If f(x) is an even function, where f(x) ≠ 0, then which one of the following is correct?a)f′ (x) is even functionb)f′ (x) is odd functionc)f′ (x) may be an even or odd function depending on the type of functiond)f′ (x) is a constant functionCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If f(x) is an even function, where f(x) ≠ 0, then which one of the following is correct?a)f′ (x) is even functionb)f′ (x) is odd functionc)f′ (x) may be an even or odd function depending on the type of functiond)f′ (x) is a constant functionCorrect answer is option 'B'. Can you explain this answer?.
If f(x) is an even function, where f(x) ≠ 0, then which one of the following is correct?a)f′ (x) is even functionb)f′ (x) is odd functionc)f′ (x) may be an even or odd function depending on the type of functiond)f′ (x) is a constant functionCorrect answer is option 'B'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about If f(x) is an even function, where f(x) ≠ 0, then which one of the following is correct?a)f′ (x) is even functionb)f′ (x) is odd functionc)f′ (x) may be an even or odd function depending on the type of functiond)f′ (x) is a constant functionCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If f(x) is an even function, where f(x) ≠ 0, then which one of the following is correct?a)f′ (x) is even functionb)f′ (x) is odd functionc)f′ (x) may be an even or odd function depending on the type of functiond)f′ (x) is a constant functionCorrect answer is option 'B'. Can you explain this answer?.
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