Question:
Let \( f(x) = \sqrt{4 - x^2} \), \( g(x) = \sqrt{x^2 - 1} \).
Then the domain of the function \( h(x) = f(x) + g(x) \) is equal to:
Let \( f(x) = \sqrt{4 - x^2} \), \( g(x) = \sqrt{x^2 - 1} \). Then the domain of the function \( h(x) = f(x) + g(x) \) is equal to:
Show Hint
To find the domain of a composite function, determine the common domain for all functions involved.
Updated On: Apr 8, 2026
- \( (-\infty, -1] \cup [1, \infty) \)
- \( (-\infty, -2] \cup [2, \infty) \)
- \( [-2, -1] \cup [1, 2] \)
- \( [-2, 1] \cup [1, 2] \)
- \( [1, 2] \)
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The Correct Option is D
Solution and Explanation
The domain of \( f(x) = \sqrt{4 - x^2} \) is \( -2 \leq x \leq 2 \), and the domain of \( g(x) = \sqrt{x^2 - 1} \) is \( x \leq -1 \) or \( x \geq 1 \). For the function \( h(x) = f(x) + g(x) \) to be defined, the domain must satisfy both conditions: Thus, the domain of \( h(x) \) is \( [-2, 1] \cup [1, 2] \).
Thus, the correct answer is (D).
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