Let f(x) = |x| be a function with domain [-6, 4] and let g(x) = |2x + 3|, Then the domain of (fog)(x) is
Explanation:
(fog)(x) = f[g(x)] = f(|2x + 3|)
Since the domain of f(x) is [-6, 4]
⇒ -6 ≤ |2x + 3| ≤ 4
Since |2x + 3| ≥ 0
⇒ |2x + 3| ≤ 4
⇒ -4 ≤ 2x + 3 ≤ 4
⇒ -7 ≤ 2x ≤ 1
⇒ -3.5 ≤ x ≤ 0.5
∴ Domain of fog(x) is [-7/2, 1/2]
Hence, option (b).
» Your doubt will be displayed only after approval.
Help us build a Free and Comprehensive Preparation portal for various competitive exams by providing us your valuable feedback about Apti4All and how it can be improved.