The set of all x for which log (1 + x) £ x is | MATH - INCREASING AND DECREASING FUNCTION | SolveeIt

The set of all x for which log (1 + x) £ x is

(0, )

(–1, )

(–1, 0)

None of these

Answer

(–1, )

Explanation

f(x) = log(1 + x) – x ; f ¢(x) = $\frac{1}{1 + x} - 1 = \frac{- x}{1 + x}$

If x > 0 Ž f ¢(x) < 0

Ž f(x) is Æ If –1 < x £ 0

Ž f ¢(x) ³ 0 Ž f

Q x £ 0 Ž f(x) £ f(0) (f(0) = 0)

Ž f(x) £ 0 Ž log (1 + x) £ x

Question: The set of all x for which log (1 + x) £ x is...