Question

Find the domain of under root of a square minus x square where a is greater than 0

Answer 1

Answer:

Concept:

Relations and functions

Step-by-step explanation:

Given:

$\sqrt{a^{2}-x^{2}}(a \geq 0)$

Find:

$\text { Domain of } \sqrt{a^{2}-x^{2}}(a \geq 0)$

Solution:

$Let f(x)=\sqrt{a^{2}-x^{2}}$

$\begin{aligned}&\Rightarrow \quad(a+x) \cdot(a-x) \geq 0 . \\&\Rightarrow \quad-(a+x)(x-a) \geq 0 \\&\Rightarrow \quad(x-a) \cdot(x+a) \leq 0\end{aligned}$

$\begin{gathered}a^{2}-x^{2} \geq 0 \\a^{2} \geq x^{2} \\a \geq x,-a \leq x \\x=[-a, a]\end{gathered}$

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