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Can someone please help me find the domain of this function

Can someone please help me find the domain of this function-example-1
User Dream Lane
by
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1 Answer

6 votes

Given the function,


t(v) = \sqrt{ {v}^(2) + 2v - 8 }

We are aware that square root function is defined for only non negative values.

So,


\to {v}^(2) + 2v - 8 \geqslant 0


\to{v}^(2) + 4v - 2v- 8 \geqslant 0


\to {v}(v + 4) - 2(v + 4) \geqslant 0


\to(v + 4)(v - 2) \geqslant 0

Therefore,


\boxed{\red{v\in (-\infty, -4] \cup [2,\infty})}

Since this is the possible input values of v for which the given function is defined, it is the domain of the function.

User Demonchand
by
7.1k points
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