If `f(x) = x/sqrt(1 + x^2)`, then `(fofof )(x) =`
a)`(3x)/(sqrt(1+x^2)`
b)x/sqrt(1+3x^2)`
c)`(3x)/(sqrt(1+x^2)`
d)None of these

Explanation

(b) `(fofof)(x) = (fof) (f(x))`
`= (fof) (x/(sqrt(1+x^2))) = f[(x/sqrt(1+x^2))]/sqrt(1+x^2/(1+x^2))`
`=f ((xsqrt(1+x^2))/(sqrt(1+x^2) sqrt(1+2x^2)) = f(x/sqrt(1+2x^2))`
`= x/sqrt(1+2x^2) "/" sqrt[1+ x^2/(1+2x^2)] = x/sqrt(1+3x^2)`