G(×)=x²-2. How to find the range and domain
Answers
Answer:
How do you find the domain and range of
g
(
x
)
=
x
x
2
−
16
?
Algebra Domain and Range of a Function
2 Answers
Narad T.
Mar 17, 2018
The domain of
g
(
x
)
is
x
∈
R
−
{
−
4
,
4
}
.
The range is
g
(
x
)
∈
R
Explanation:
As you cannot divide by
0
, the denominator is
≠
0
Therefore,
x
2
−
16
≠
0
,
⇒
x
≠
−
4
and
x
≠
4
The domain of
g
(
x
)
is
x
∈
R
−
{
−
4
,
4
}
To calculate the range, proceed as follows
Let
y
=
x
x
2
−
16
y
(
x
2
−
16
)
=
x
y
x
2
−
x
−
16
y
=
0
This is a quadratic equation in
x
, and in order to have solutions,
the discriminant
≥
0
a
=
y
b
=
−
1
c
=
−
16
y
Δ
=
b
2
−
4
a
c
=
(
−
1
)
2
−
4
(
y
)
(
−
16
y
)
=
1
+
64
y
2
∀
y
∈
R
,
⇒
,
Δ
≥
0
Therefore,
The range is
g
(
x
)
∈
R
graph{x/(x^2-16) [-10, 10, -5, 5]}
Step-by-step explanation:
domain of a function f(x) is the set of all values for which the function is defined, and the range of the function is the set of all values that f takes. A rational function is a function of the form f(x)=p(x)q(x) , where p(x) and q(x) are polynomials and q(x)≠0 .