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