JEE Mains · Maths · STD 11- 2. Relation and Function
If the domain of the function \(f(x)=\frac{\sqrt{x^2-25}}{\left(4-x^2\right)}\) \(+\log _{10}\left(x^2+2 x-15\right)\) is \((-\infty, \alpha) U[\beta, \infty)\), then \(\alpha^2+\beta^3\) is equal to :
- A \(140\)
- B \(175\)
- C \(150\)
- D \(125\)
Answer & Solution
Correct Answer
(C) \(150\)
Step-by-step Solution
Detailed explanation
\( f(x)=\frac{\sqrt{x^2-25}}{4-x^2}+\log _{10}\left(x^2+2 x-15\right) \) \( \text { Domain : } x^2-25 \geq 0 \Rightarrow x \in(-\infty,-5] \cup[5, \infty) \) \( 4-x^2 \neq 0 \Rightarrow x \neq\{-2,2\} \) \( x^2+2 x-15>0 \Rightarrow(x+5)(x-3)>0 \)…
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