MHT CET · Maths · Functions
The domain of a function \(f(y)=\frac{\cos ^{-1}(y-5)}{\sqrt{25-y^{2}}}\) is
- A \((4,6]\)
- B \((-5,5)\)
- C \([4,5)\)
- D \((4,5]\)
Answer & Solution
Correct Answer
(C) \([4,5)\)
Step-by-step Solution
Detailed explanation
We have \(f(y)=\frac{\cos ^{-1}(y-5)}{\sqrt{25-y^{2}}}\)
Here \(-1 \leq y-5 \leq 1\) and \(25-y^{2}>0\) \(\therefore \quad 4 \leq y \leq 6 \quad\) and \(\quad-5 < y < 5\) Hence domain of \(f(y)\) is \([4,5)\)
Here \(-1 \leq y-5 \leq 1\) and \(25-y^{2}>0\) \(\therefore \quad 4 \leq y \leq 6 \quad\) and \(\quad-5 < y < 5\) Hence domain of \(f(y)\) is \([4,5)\)
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