If x > 0, then which one is correct?

Category: QuestionsIf x > 0, then which one is correct?
Editor">Editor Staff asked 11 months ago

If x > 0, then which one is correct?
 
(a) x > log(x + 1)
 
(b) x < log (x + 1)
 
(c) x = log(x + 1)
 
(d) x ≥ log(x + 1)
 
I got this question in an interview.
 
My question comes from Calculus Application topic in section Application of Calculus of Mathematics – Class 12
NCERT Solutions for Subject Clas 12 Math Select the correct answer from above options 
Interview Questions and Answers, Database Interview Questions and Answers for Freshers and Experience

1 Answers
Editor">Editor Staff answered 11 months ago

Right choice is (a) x > log(x + 1)
 
The explanation is: Assume, f(x) = x – log(1 + x)
 
Therefore, f’(x) = 1 – (1/(1 + x))
 
= x/(x + 1) > 0, when x > 0
 
Hence, we must have, f(x) > f(0), when x > 0
 
But f(0) = 0 – log1 = 0
 
Thus, f(x) > 0, when x > 0 i.e.,
 
x – log(1 + x) > 0, when x > 0
 
Or x > (1 + x), when x > 0.