Question:
Find the domain of the function:
\[ f(x) = \sin^{-1}(x^2) \]
Concept:
For \( \sin^{-1}(t) \) to be defined:
\[ -1 \leq t \leq 1 \]
—Solution:
Step 1: Apply condition
\[ -1 \leq x^2 \leq 1 \]
Step 2: Solve inequality
Since \( x^2 \geq 0 \), the condition becomes:
\[ 0 \leq x^2 \leq 1 \]
Taking square roots:
\[ -1 \leq x \leq 1 \]
—Final Answer:
\[ \boxed{[-1, 1]} \]