If `f:R to R ` be defined by `f(x) = (x)/(sqrt(1 +x^(2) )),` then `(fofof)(x)= …………. .`

Answer

N/a

Explanation

Given that, `f(x) = (x)/(sqrt(1 +x^(2) ))`
`(fofof)(x)=f[f{f(x)}]`
`= f[f((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(2x^(2))+1)))]=f((x)/(sqrt(1+2x^(2))))`
`=((x)/(sqrt(1+2x^(2))))/(sqrt(1+(x^(2))/(1+2x^(2))))=(xsqrt(1+2x^(2)))/(sqrt(1+2x^(2))sqrt(1+3x^(2)))`
`=(x)/(sqrt(1+3x^(2)))=(x)/(sqrt(3x^(2)+1))`