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Let ψ1 : [0, ∞) → R, ψ2 : [0, ∞) → R, f : (0, ∞) → R and g : [0, ∞) → R be functions such that
f(0) = g(0) = 0,
Q. Which of the following statements is TRUE?
  • a)
  • b)
    For every x > 1, there exists an α ∈ (1, x) such that ψ1 (x) = 1 + αx.
  • c)
    For every x > 0, there exists a β ∈(0, x) such that ψ2 (x)  = 2x (ψ1(β) - 1).
  • d)
    f is an increasing function on the interval .
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
Let ψ1 : [0,∞)→ R,ψ2 : [0,∞)→ R, f : (0,...

Since ψ2(x) is a continuous and differentiable function ∀ x ∈ [0, x]

Hence according to LMVT there exist atleast one β ∈(0, x) such that 
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Let ψ1 : [0,∞)→ R,ψ2 : [0,∞)→ R, f : (0,∞)→ R and g : [0,∞)→ R be functions such thatf(0) = g(0) = 0,Q.Which of the following statements is TRUE?a)b)For every x > 1, there exists an α ∈ (1, x) such thatψ1 (x) = 1 + αx.c)For every x > 0, there exists a β ∈(0, x) such that ψ2 (x) = 2x (ψ1(β) - 1).d)f is an increasing function on the interval.Correct answer is option 'C'. Can you explain this answer?
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Let ψ1 : [0,∞)→ R,ψ2 : [0,∞)→ R, f : (0,∞)→ R and g : [0,∞)→ R be functions such thatf(0) = g(0) = 0,Q.Which of the following statements is TRUE?a)b)For every x > 1, there exists an α ∈ (1, x) such thatψ1 (x) = 1 + αx.c)For every x > 0, there exists a β ∈(0, x) such that ψ2 (x) = 2x (ψ1(β) - 1).d)f is an increasing function on the interval.Correct answer is option 'C'. 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 ψ1 : [0,∞)→ R,ψ2 : [0,∞)→ R, f : (0,∞)→ R and g : [0,∞)→ R be functions such thatf(0) = g(0) = 0,Q.Which of the following statements is TRUE?a)b)For every x > 1, there exists an α ∈ (1, x) such thatψ1 (x) = 1 + αx.c)For every x > 0, there exists a β ∈(0, x) such that ψ2 (x) = 2x (ψ1(β) - 1).d)f is an increasing function on the interval.Correct answer is option 'C'. 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 ψ1 : [0,∞)→ R,ψ2 : [0,∞)→ R, f : (0,∞)→ R and g : [0,∞)→ R be functions such thatf(0) = g(0) = 0,Q.Which of the following statements is TRUE?a)b)For every x > 1, there exists an α ∈ (1, x) such thatψ1 (x) = 1 + αx.c)For every x > 0, there exists a β ∈(0, x) such that ψ2 (x) = 2x (ψ1(β) - 1).d)f is an increasing function on the interval.Correct answer is option 'C'. Can you explain this answer?.
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