Domain of function f(x) = sin^{-1}(5x) is | vedclass

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Question

(B) The domain of the function $f(x) = \sin^{-1}(u)$ is defined by the condition $-1 \le u \le 1$.For the given function $f(x) = \sin^{-1}(5x)$,we set

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$[-\frac{1}{5}, \frac{1}{5}]$

Vedclass · Answer

(B) The domain of the function $f(x) = \sin^{-1}(u)$ is defined by the condition $-1 \le u \le 1$.For the given function $f(x) = \sin^{-1}(5x)$,we set $u = 5x$.Thus,the condition becomes $-1 \le 5x \le 1$.Dividing the entire inequality by $5$,we get $-\frac{1}{5} \le x \le \frac{1}{5}$.Therefore,the domain of the function is $[-\frac{1}{5}, \frac{1}{5}]$.

Domain of function $f(x) = \sin^{-1}(5x)$ is

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