Question:
The domain of \( f(x) = \cos^{-1}(7x) \) is:
The domain of \( f(x) = \cos^{-1}(7x) \) is:
Updated On: Mar 27, 2025
- \( \left[ -\frac{1}{7}, \frac{1}{7} \right] \)
- \( [-7, 7] \)
- \( [0, 7] \)
- \( [-1, 1] \)
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The Correct Option is A
Solution and Explanation
The function \( \cos^{-1}(x) \) is defined only for \( x \in [-1, 1] \). Here, \( f(x) = \cos^{-1}(7x) \), so \( 7x \) must also lie in the interval \([-1, 1]\). Solve the inequality:
\(-1 \leq 7x \leq 1\).
Divide through by 7:
\(-\frac{1}{7} \leq x \leq \frac{1}{7}\).
Thus, the domain of \( f(x) = \cos^{-1}(7x) \) is \(\left[ -\frac{1}{7}, \frac{1}{7} \right]\).
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