AP EAMCET · Maths · Inverse Trigonometric Functions
The domain of \(f(x)=\cos ^{-1}\left(\frac{x-3}{2}\right)-\log _{10}(4-x)\) is
- A \((1,4)\)
- B \([1,4)\)
- C \((1,4]\)
- D \([1,4]\)
Answer & Solution
Correct Answer
(B) \([1,4)\)
Step-by-step Solution
Detailed explanation
Let \(f(x)=\cos ^{-1}\left(\frac{x-3}{2}\right)-\log _{10}(4-x)\) For domain of \(\log _{10}(4-x) \Rightarrow 4-x > 0 \Rightarrow x < 4\) For domain of \(\cos ^{-1}\left(\frac{x-3}{2}\right) \Rightarrow-1 \leq \frac{x-3}{2} \leq 1\) \(\Rightarrow \quad 1 \leq x \leq 5\) Now…
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