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Question

Mathematics Question on Matrices

The domain of f(x)=cos1(7x)f(x) = \cos^{-1}(7x) is:

A

[17,17]\left[ -\frac{1}{7}, \frac{1}{7} \right]

B

[7,7][-7, 7]

C

[0,7][0, 7]

D

[1,1][-1, 1]

Answer

[17,17]\left[ -\frac{1}{7}, \frac{1}{7} \right]

Explanation

Solution

The function cos1(x)\cos^{-1}(x) is defined only for x[1,1]x \in [-1, 1]. Here, f(x)=cos1(7x)f(x) = \cos^{-1}(7x), so 7x7x must also lie in the interval [1,1][-1, 1]. Solve the inequality:

17x1-1 \leq 7x \leq 1.

Divide through by 7:

17x17-\frac{1}{7} \leq x \leq \frac{1}{7}.

Thus, the domain of f(x)=cos1(7x)f(x) = \cos^{-1}(7x) is [17,17]\left[ -\frac{1}{7}, \frac{1}{7} \right].