Question

Find the domain of h(x)=x/x^2-x-6​

Answer 1

Set the denominator equal to 0 and solve for x.

x^2 - x - 6 = 0

Factor.

(x - 3)(x + 2 ) = 0

Set each factor to 0 and solve for x.

x - 3 = 0

x = 3

x + 2 = 0

x = -2

The domain is ALL REAL NUMBERS except that x CANNOT equal 3 or -2.

Answer 2

Answer:

x

∈

R

−

{

−

2

.

3

}

Explanation:

h

(

x

)

=

x

x

2

−

x

−

6

is defined for all Real values of

x

except those values for which

x

2

−

x

−

6

=

0

x

2

−

x

−

6

=

(

x

+

2

)

(

x

−

3

)

So if

x

=

−

2

or

x

=

3

XXXX

x

2

−

x

−

6

=

0

and

XXXX

h

(

x

)

is undefined