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Write the domain of the real function f ...

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

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We have, `{f}({x})=sqrt{25-{x}^{2}}`

The function is defined only when, `25-x^{2} geq 0`

`Rightarrow 25-x^{2}=0 `

`Rightarrow(5)^{2}-(x)^{2}=0 `

`Rightarrow(5+x)(5-x)=0 `

`Rightarrow 5+x=0 text { and } 5-x=0 `

`Rightarrow x in[-5,5] quad[text { Since, } x in R]`

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