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Let f : R → R be a function defined by f (x) = min {x + 1, |x| + 1}, Then which of the following is true?
  • a)
    f (x) is differentiable everywhere
  • b)
    f (x) is not differentiable at x = 0
  • c)
    f (x) > 1 for all x ∈ R
  • d)
    f (x) is not differentiable at x = 1    
Correct answer is option 'A'. Can you explain this answer?
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Let f : R → R be a function defined by f (x) = min {x + 1, |x| +...
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Let f : R → R be a function defined by f (x) = min {x + 1, |x| +...
Explanation:

Given Function:
f(x) = min {x + 1, |x| + 1}

Differentiability:
- To determine the differentiability of the function f(x), we need to check if the function is continuous and has a well-defined derivative at each point in its domain.
- In this case, the function f(x) is a piecewise function where it takes the minimum value between x + 1 and |x| + 1.
- Both x + 1 and |x| + 1 are continuous functions for all real numbers x.

Analysis:
- At x = 0, f(0) = min {0 + 1, |0| + 1} = min {1, 1} = 1
- For x < 0,="" f(x)="x" +="" />
- For x > 0, f(x) = |x| + 1
- The function f(x) is continuous everywhere.
- At x = 0, the function is differentiable because both x + 1 and |x| + 1 have well-defined derivatives at x = 0.

Conclusion:
- The function f(x) = min {x + 1, |x| + 1} is differentiable everywhere in its domain R.
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Let f : R → R be a function defined by f (x) = min {x + 1, |x| + 1}, Then which of the following is true?a)f (x) is differentiable everywhereb)f (x) is not differentiable at x = 0c)f (x) >1 for all x ∈ Rd)f (x) is not differentiable at x = 1 Correct answer is option 'A'. Can you explain this answer?
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Let f : R → R be a function defined by f (x) = min {x + 1, |x| + 1}, Then which of the following is true?a)f (x) is differentiable everywhereb)f (x) is not differentiable at x = 0c)f (x) >1 for all x ∈ Rd)f (x) is not differentiable at x = 1 Correct answer is option 'A'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Let f : R → R be a function defined by f (x) = min {x + 1, |x| + 1}, Then which of the following is true?a)f (x) is differentiable everywhereb)f (x) is not differentiable at x = 0c)f (x) >1 for all x ∈ Rd)f (x) is not differentiable at x = 1 Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let f : R → R be a function defined by f (x) = min {x + 1, |x| + 1}, Then which of the following is true?a)f (x) is differentiable everywhereb)f (x) is not differentiable at x = 0c)f (x) >1 for all x ∈ Rd)f (x) is not differentiable at x = 1 Correct answer is option 'A'. Can you explain this answer?.
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