AP EAMCET · Maths · Functions
The domain of the real valued function \(f(x)=\frac{\log _2(x+3)}{\sqrt{x^2+3 x+2}}\) is
- A \((-3, \infty)\)
- B \((-3,-1) \cup(-1, \infty)\)
- C \((-3,-2) \cup(-2,-1) \cup(-1, \infty)\)
- D \((-3,-2) \cup(-1, \infty)\)
Answer & Solution
Correct Answer
(D) \((-3,-2) \cup(-1, \infty)\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { Given, } f(x)=\frac{\log _2(x+3)}{\sqrt{x^2+3 x+2}} \\ & \\ & \quad x^2+3 x+2>0 \\ & \Rightarrow \quad x^2+2 x+x+2>0 \\ & \Rightarrow \quad x(x+2)+1(x+2)>0 \\ & \Rightarrow \quad(x+2)(x+1)>0 \\ & \Rightarrow \quad x \in(-\infty,-2) \cup(-1, \infty) \\ &…
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