Let f be a function with domain [–3, 5] and let g(x) = |3x + 4|. Then the domain of (fog)(x) is

$\left[-3, \frac{1}{3}\right]$

$f(g(x))⇒-3≤|3x+4|≤5$  (Negative not considered due to modules)

$⇒|3x+4|≤5$

so $-5≤3x+4≤5$

$(fog)(x)=f[g(x)]=f(|3 x+4|)$

$\Rightarrow-5 \leq 3 x+4 \leq 5$

$\Rightarrow-9 \leq 3 x \leq 1$

$\Rightarrow-3 \leq x \leq 1 / 3$

∴ Domain of fog is $\left[-3, \frac{1}{3}\right]$

Hence (2) is the correct answer.