COMEDK · Maths · 23. Inverse Trigonometric Functions
\(\text { Let } f(x)=\cos ^{-1}(3 x-1) \text {, then domain of } f(x) \text { is equal to }\)
- A \(\left(0, \dfrac{2}{3}\right)\)
- B \(\left[-\dfrac{2}{3}, \dfrac{2}{3}\right]\)
- C \(\left(-\dfrac{2}{3}, \dfrac{2}{3}\right)\)
- D \(\left[0, \dfrac{2}{3}\right]\)
Answer & Solution
Correct Answer
(D) \(\left[0, \dfrac{2}{3}\right]\)
Step-by-step Solution
Detailed explanation
The function \(f(x) = \cos^{-1}(3x - 1)\) is defined when the argument of the inverse cosine function lies in the interval \([-1, 1]\). Therefore, we set the inequality: \(-1 \le 3x - 1 \le 1\) Adding \(1\) to all parts of the inequality: \(-1 + 1 \le 3x - 1 + 1 \le 1 + 1\)…
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