MCQ
આપેલ પૈકી . . . . યુગ્મ વિધેય છે.
- 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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