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

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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.