Find the domain of h(x)=x/x^2-x-6
2 answers:
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:
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
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