Question

A function is $\sqrt[2]{((x+5)(x-3)(4-x))}$ . Find its domain.

Answer 1

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, ∞ )