KCET · Maths · Functions
The domain of the function \( f: R \rightarrow R \) defined by \( f(x)=\sqrt{x^{2}-7 x+12} \) is
- A \((-\infty, 3] \cup(4, \infty) \)
- B \( (3,4) \)
- C \((-\infty, 3] \cup[4, \infty) \)
- D \((-\infty, 3] \cap[4, \infty) \)
Answer & Solution
Correct Answer
(C) \((-\infty, 3] \cup[4, \infty) \)
Step-by-step Solution
Detailed explanation
\((C)\)
\(f(x)=\sqrt{x^{2}-7 x+12}\)
\(x^{2}-7 x+12 \geq 0\)
\((x-4)(x-3) \geq 0\)
\(\Rightarrow x \in(-\infty, 3] \cup[4, \infty)\)
\(f(x)=\sqrt{x^{2}-7 x+12}\)
\(x^{2}-7 x+12 \geq 0\)
\((x-4)(x-3) \geq 0\)
\(\Rightarrow x \in(-\infty, 3] \cup[4, \infty)\)
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