Let f(x) be a function whose domain is [-5, 7]. Then the domain of f(|2x + 5|) is :

[-6, 1]

⇒ −5 ≤ |2x + 5| ≤ 7

|2x + 5| ≥ -5 and |2x + 5| ≤ 7

always true and -7 ≤ 2x + 5 ≤ 7

-6 ≤ x ≤ 1

Hence domain is [–6, 1].

Hence (1) is the correct answer.

Key concept: If domain of f(x) is [a, b] then the domain of f(g(x)) is values of x for which g(x) ∈ [a, b]