Question

What is the domain of the function? f(x)=
`(x-3)/(2x^(2)+x-21 )` (−∞,3)∪(3,∞) (−∞,−3)∪(−3,72)∪(72,∞) (−∞,−72)∪(−72,∞) (−∞,−72)∪(−72,3)∪(3,∞)

Answer 1

(−∞,−7/2)∪(−7/2,3)∪(3,∞)

Explanation:

(x-3)

----------------

2x^2 +x -21

First factor the denominator

(x-3)

----------------

( 2x +7) (x-3)

The domain is restricted when the denominator goes to zero

2x+7 =0 x-3 =0

2x = -7 x-3=0

x = -7/2 x =3

This two points are not in the domain

(−∞,−7/2)∪(−7/2,3)∪(3,∞)