FunctionHard
Question
Let f(x) be a function whose domain is [- 5, 7]. Let g(x) = |2x + 5|, then domain of (fog) (x) is
Options
A.[- 4, 1]
B.[- 5, 1]
C.[- 6, 1]
D.none of these
Solution
Domain of f(g(x))
Range of g(x) ≡ Domain of f(x)
⇒ - 5 ≤ |2x + 5| ≤ 7
⇒ 0 ≤ |2x + 5| ≤ 7
⇒ -7 ≤ 2x + 5 ≤ 7
⇒ - 12 ≤ 2x ≤ 2
⇒ - 6 ≤ x ≤ 1
Range of g(x) ≡ Domain of f(x)
⇒ - 5 ≤ |2x + 5| ≤ 7
⇒ 0 ≤ |2x + 5| ≤ 7
⇒ -7 ≤ 2x + 5 ≤ 7
⇒ - 12 ≤ 2x ≤ 2
⇒ - 6 ≤ x ≤ 1
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