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Step 1: Understand the function
The function is $f(x) = \sin^{-1}x$, which is the inverse sine function. The domain is restricted to $x \in [-\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}]$.
Step 2: Determine key points for graphing
We need to find the values of $f(x)$ at the endpoints of the domain and at some intermediate points.
Step 3: Sketch the graph
The graph of $f(x) = \sin^{-1}x$ is a curve that passes through the points $(-\frac{1}{\sqrt{2}}, -\frac{\pi}{4})$, $(0, 0)$, and $(\frac{1}{\sqrt{2}}, \frac{\pi}{4})$. Since the domain is restricted, we only consider the portion of the graph within the given interval.
The graph will be an increasing function within the given domain.
Step 4: Determine the range
The range of $f(x)$ is the set of all possible values of $f(x)$ for $x$ in the given domain. Since $f(x)$ is continuous and increasing on the interval $[-\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}]$, the range is the interval between the values of $f(x)$ at the endpoints.
The range is $[-\frac{\pi}{4}, \frac{\pi}{4}]$.
Correct Answer: Range: $[-\frac{\pi}{4}, \frac{\pi}{4}]$<\/strong>