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
Create a free account to view solution
View Solution FreeMore Function Questions
If f(x) = 3, then values of f(x) lie in -...Let $\alpha,\beta$ be the roots of the quadratic equation $12x^{2} - 20x + 3\lambda = 0,\lambda \in \mathbb{Z}$. If $\fr...The value of b and c for which the identity f ( x + 1) - f (x) = 8x + 3 is satisfied, where f(x) = bx2 + cx + d, are -...Suppose, f(x) = (x + 1)2 for x ≥ - 1 If g (x) is the function whose graph is reflection of the graph of f (x) with...The period of sin4 x + cos4 x is -...