Question

If f(x)=x/√1+x², then (fo(fof))(x)=.......,Select Proper option from the given options.
(a) x/1+x²
(b)1+x²/x
(c) x/√1+2x²
(d) x/√1+3x²

Answer 1

Option D is the correct option for this function.

Answer 2

Given, $f(x)=\frac{x}{\sqrt{1+x^2}}$

first of all, we should find fof(x) = f(f(x))
so, $f(f(x))=\frac{\frac{x}{\sqrt{1+x^2}}}{\sqrt{1+\frac{x^2}{1+x^2}}}$

=$\frac{x}{\sqrt{1+2x^2}}$

now, find (fo(fof))(x) ,
f(f(f(x))) = $f\{\frac{x}{\sqrt{1+2x^2}}\}$

$=\frac{\frac{x}{\sqrt{1+2x^2}}}{\sqrt{1+\frac{x^2}{1+2x^2}}}$

=$\frac{x}{\sqrt{1+3x^2}}$

hence, option (d) is correct.