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Which one of the following is correct in respect of the function f: R → R+ defined as f(x) = |x + 1|?
- a)f(x2) = |f(x)|2
- b)f(|x|) = |f(x)|
- c)f(x + y) = f(X) + f(y)
- d)None of the above
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
Which one of the following is correct in respect of the function f: R ...
Calculation:
Given that,
⇒ f(x) = |x + 1|
first option
⇒ f(x2) = |x2 + 1|
⇒ f(x)2 = |x + 1|2
so we can say that
⇒ f(x2) = |f(x)|2
⇒ |x + 1|2 ≠ |x2 + 1|
First option not correct.
Second option,
⇒ f(|x|) = |f(x)|
⇒ f(|x|) = ||x| + 1|
⇒ |f(x)| = ||x + 1|| = |x + 1|
f(|x|) ≠ |f(x)| because ||x| + 1| ≠ |x + 1| for real values of x.
Third option,
⇒ f(x + y) = f(X) + f(y)
⇒ f(x + y) = |(x + y) + 1|
⇒ f(y) = |y + 1|
so,
⇒ |(x + y) + 1| ≠ |x + 1| + |y + 1|
So f(x + y) ≠ f(x) + f(y)
Given that,
⇒ f(x) = |x + 1|
first option
⇒ f(x2) = |x2 + 1|
⇒ f(x)2 = |x + 1|2
so we can say that
⇒ f(x2) = |f(x)|2
⇒ |x + 1|2 ≠ |x2 + 1|
First option not correct.
Second option,
⇒ f(|x|) = |f(x)|
⇒ f(|x|) = ||x| + 1|
⇒ |f(x)| = ||x + 1|| = |x + 1|
f(|x|) ≠ |f(x)| because ||x| + 1| ≠ |x + 1| for real values of x.
Third option,
⇒ f(x + y) = f(X) + f(y)
⇒ f(x + y) = |(x + y) + 1|
⇒ f(y) = |y + 1|
so,
⇒ |(x + y) + 1| ≠ |x + 1| + |y + 1|
So f(x + y) ≠ f(x) + f(y)
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Community Answer
Which one of the following is correct in respect of the function f: R ...
Function Properties:
- f(x) = |x + 1|
Explanation:
- The function f: R → R+ is defined as f(x) = |x + 1|.
- The absolute value function |x| returns the positive value of x.
- So, f(x) will always return a positive value.
Analysis of Options:
- a) f(x^2) = |f(x)|^2: This statement is not true. Squaring the function f(x) does not equal the absolute value of f(x) squared.
- b) f(|x|) = |f(x)|: This statement is not true. The function f(|x|) does not necessarily equal the absolute value of f(x).
- c) f(x + y) = f(x) + f(y): This statement is not true. The function f(x + y) does not equal f(x) + f(y) for this specific function f(x) = |x + 1|.
Correct Answer:
- None of the above (D): None of the provided options accurately represent the properties of the given function f(x) = |x + 1|. Therefore, the correct answer is option D.
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Which one of the following is correct in respect of the function f: R → R+defined as f(x) = |x + 1|?a)f(x2) = |f(x)|2b)f(|x|) = |f(x)|c)f(x + y) = f(X) + f(y)d)None of the aboveCorrect answer is option 'D'. Can you explain this answer?
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