MCQ
If $f(x) = \frac{x}{{\sqrt {1 + {x^2}} }}$, then $(fofof)(x) = $
- A$\frac{{3x}}{{\sqrt {1 + {x^2}} }}$
- ✓$\frac{x}{{\sqrt {1 + 3{x^2}} }}$
- C$\frac{{3x}}{{\sqrt {1 + {x^2}} }}$
- DNone of these
$ = f\,\left[ {\frac{{\left( {\frac{x}{{\sqrt {1 + {x^2}} }}} \right)}}{{\sqrt {1 + \frac{{{x^2}}}{{1 + {x^2}}}} }}} \right] $
$= f\,\left( {\frac{{x\sqrt {1 + {x^2}} }}{{\sqrt {1 + {x^2}} \sqrt {1 + 2{x^2}} }}} \right)$
$ = f\,\left( {\frac{x}{{\sqrt {1 + 2{x^2}} }}} \right) $
$= \frac{{\frac{x}{{\sqrt {1 + 2{x^2}} }}}}{{\sqrt {\left[ {1 + \frac{{{x^2}}}{{1 + 2{x^2}}}} \right]} }} $
$= \frac{x}{{\sqrt {1 + 3{x^2}} }}.$
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