Year 12 Exam  >  Year 12 Questions  >  The true set of real values of x for which th... Start Learning for Free
The true set of real values of x for which the function, f(x) = x ln x – x + 1 is positive is
  • a)
     (1, ∞)
  • b)
    (1/e, ∞)
  • c)
    [e, ∞)
  • d)
    (0, 1) and (1, ∞)
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
The true set of real values of x for which the function, f(x) = xln x ...
f(x)=xlnx−x+1
f(1)=0
On differentiating w.r.t x, we get
f′(x)=x*1/x+lnx−1
=lnx
Therefore,f′(x)>0 for allx∈(1,∞)
f′(x)<0 for allx∈(0,1)
lim x→0 f(x)=1
f(x)>0
for allx∈(0,1)∪(1,∞)
View all questions of this test
Most Upvoted Answer
The true set of real values of x for which the function, f(x) = xln x ...
The true set of real values of x for which the function f(x) = xln x is defined is x > 0. This is because the natural logarithm function ln x is only defined for positive real numbers.
Explore Courses for Year 12 exam

Top Courses for Year 12

The true set of real values of x for which the function, f(x) = xln x –x + 1 is positive isa)(1, ∞)b)(1/e, ∞)c)[e, ∞)d)(0, 1) and (1, ∞)Correct answer is option 'D'. Can you explain this answer?
Question Description
The true set of real values of x for which the function, f(x) = xln x –x + 1 is positive isa)(1, ∞)b)(1/e, ∞)c)[e, ∞)d)(0, 1) and (1, ∞)Correct answer is option 'D'. Can you explain this answer? for Year 12 2025 is part of Year 12 preparation. The Question and answers have been prepared according to the Year 12 exam syllabus. Information about The true set of real values of x for which the function, f(x) = xln x –x + 1 is positive isa)(1, ∞)b)(1/e, ∞)c)[e, ∞)d)(0, 1) and (1, ∞)Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Year 12 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The true set of real values of x for which the function, f(x) = xln x –x + 1 is positive isa)(1, ∞)b)(1/e, ∞)c)[e, ∞)d)(0, 1) and (1, ∞)Correct answer is option 'D'. Can you explain this answer?.
Solutions for The true set of real values of x for which the function, f(x) = xln x –x + 1 is positive isa)(1, ∞)b)(1/e, ∞)c)[e, ∞)d)(0, 1) and (1, ∞)Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Year 12. Download more important topics, notes, lectures and mock test series for Year 12 Exam by signing up for free.
Here you can find the meaning of The true set of real values of x for which the function, f(x) = xln x –x + 1 is positive isa)(1, ∞)b)(1/e, ∞)c)[e, ∞)d)(0, 1) and (1, ∞)Correct answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of The true set of real values of x for which the function, f(x) = xln x –x + 1 is positive isa)(1, ∞)b)(1/e, ∞)c)[e, ∞)d)(0, 1) and (1, ∞)Correct answer is option 'D'. Can you explain this answer?, a detailed solution for The true set of real values of x for which the function, f(x) = xln x –x + 1 is positive isa)(1, ∞)b)(1/e, ∞)c)[e, ∞)d)(0, 1) and (1, ∞)Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of The true set of real values of x for which the function, f(x) = xln x –x + 1 is positive isa)(1, ∞)b)(1/e, ∞)c)[e, ∞)d)(0, 1) and (1, ∞)Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice The true set of real values of x for which the function, f(x) = xln x –x + 1 is positive isa)(1, ∞)b)(1/e, ∞)c)[e, ∞)d)(0, 1) and (1, ∞)Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice Year 12 tests.
Explore Courses for Year 12 exam

Top Courses for Year 12

Explore Courses
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev