Question

The set of all x for which (1 + x) ≤ x is equal to ... 

Answer 1

Let f(x) = ln(1 + x) – x

From the sign scheme, we can say that f is decreasing for x ≥ 0

when x ≥ 0

⇒ f(x) ≤ f(0)

⇒ log(1 + x) – x ≤ 0

⇒ log(1 + x) ≤ x

Thus, log(1 + x) ≤ x, ∀ x ≥ 0