MCQ
Which of the following function is even function
- A$f(x) = \frac{{{a^x} + 1}}{{{a^x} - 1}}$
- ✓$f(x) = x\left( {\frac{{{a^x} - 1}}{{{a^x} + 1}}} \right)$
- C$f(x) = \frac{{{a^x} - {a^{ - x}}}}{{{a^x} + {a^{ - x}}}}$
- D$f(x) = \sin x$
So, it is an odd function.
In $(b)$, $f( - x) = ( - x)\frac{{{a^{ - x}} - 1}}{{{a^{ - x}} + 1}} = - x\frac{{1 - {a^x}}}{{1 + {a^x}}} = x\frac{{{a^x} - 1}}{{{a^x} + 1}} = f(x)$
So, it is an even function.
In $(c)$, $f( - x) = - \sin \left[ {\log (x + \sqrt {1 + {x^2}} )} \right]$
So, it is an odd function.
In $(d)$, $f( - x) = \sin ( - x) = - \sin x = - f(x)$
So, it is an odd function.
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$l_1:(3+ t ) \hat{ i }+(-1+2 t ) \hat{ j }+(4+2 t ) \hat{ k },-\infty< t <\infty $
$l_2:(3+2 t ) \hat{ i }+(3+2 t ) \hat{ j }+(2+ s ) \hat{ k },-\infty< s <\infty$
Then, the coordinate$(s)$ of the point$(s)$ on $l_2$ at a distance of $\sqrt{17}$ from the point of intersection of $l$ and $l_1$ is(are)
$(A)$ $\left(\frac{7}{3}, \frac{7}{3}, \frac{5}{3}\right)$ $(B)$ $(-1,,-1,0)$ $(C)$ $(1,1,1)$ $(D)$ $\left(\frac{7}{9}, \frac{7}{9}, \frac{8}{9}\right)$