Write the domain of the real function f defined by f(x)= 25-x^2 . - Vidyadip

Question

Write the domain of the real function f defined by $\text{f(x)}=\sqrt{25-\text{x}^2}.$

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Answer

We have, $\text{f(x)}=\sqrt{25-\text{x}^2}$

The function is defined only when $25-\text{x}^2\geq0$

$\text{x}^2-25\leq0$

$(\text{x}+5)(\text{x}-5)\leq0$

$\text{x}\in[-5,5]$

Therefore, the domain of the given function is [-5, 5].

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