Question

Can someone please help me find the domain of this function

Answer 1

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.