A function is ![\sqrt[2]{((x+5)(x-3)(4-x))}](https://tex.z-dn.net/?f=%5Csqrt%5B2%5D%7B%28%28x%2B5%29%28x-3%29%284-x%29%29%7D "\sqrt[2]{((x+5)(x-3)(4-x))}")
. Find its domain.
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everything comes from Square root is greater than or equal to zero.
So,
f(x) ≥ 0
==> (x+5) (x-3) (4-x) ≥ 0
Multiply by -1 both sides
==> (x + 5)(x - 3)( x - 4) ≤ 0
Critical Points :- -5 , 3 , 4
Refer to the attachment.
From the figure,
==> x € [ -5, 3 ] U [ 4, ∞ )
Attachments:
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