- Home
- Standard 12
- Mathematics
1.Relation and Function
easy
If $f(x) = \log \frac{{1 + x}}{{1 - x}}$, then $f(x)$ is
A
Even function
B
$f({x_1})f({x_2}) = f({x_1} + {x_2})$
C
$\frac{{f({x_1})}}{{f({x_2})}} = f({x_1} - {x_2})$
D
Odd function
Solution
(d) Here, $f(x) = \log \left( {\frac{{1 + x}}{{1 – x}}} \right)$
and $f( – x) = \log \left( {\frac{{1 – x}}{{1 + x}}} \right) = \log {\left( {\frac{{1 + x}}{{1 – x}}} \right)^{ – 1}}$
$ = – \log \left( {\frac{{1 + x}}{{1 – x}}} \right) = – f(x)$ ==> $f(x)$ is an odd function.
Standard 12
Mathematics
