The function f(x) = (1 + x) - 2x 2 + x is increasing on - Vidyadip

MCQ

The function $f(x) = \log (1 + x) - {{2x} \over {2 + x}}$ is increasing on

✓
(0, $\infty $)
B
($ - \infty $, 0)
C
$( - \infty ,\infty )$
D
None of these

✓

Answer

Correct option: A.

(0, $\infty $)

a
(a) $f(x) = \log (1 + x) - \frac{{2x}}{{2 + x}}$

$ \Rightarrow f'(x) = \frac{1}{{1 + x}} - \frac{{(2 + x).(2 - 2x)}}{{{{(2 + x)}^2}}}$

==> $f'(x) = \frac{{{x^2}}}{{(x + 1){{(x + 2)}^2}}}$

Obviously, $f'(x) > 0$ for all $x > 0$

Hence $f(x)$ is increasing on $(0,\infty )$.

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