what is the range of relation y=f(x)=2x+3, when the demotion is 3?
Answers
Answer:
Domain :
R
−
{
−
1
,
3
}
Range:
R
Step-by-step explanation:
To Find the domain
Equate the denominator(
x
2
−
2
x
−
3
) to zero, then solve the equation for
x
→
x
2
−
2
x
−
3
=
0
→
x
=
−
(
−
2
)
±
√
(
−
2
)
2
−
4
⋅
(
1
)
⋅
(
−
3
)
2
⋅
1
→
x
=
1
±
2
⇒
x
=
−
1
and
x
=
3
This means that, when
x
=
−
1
or
3
, we have the
x
2
−
2
x
−
3
=
0
Implying that
f
(
x
)
=
x
0
which is undefined.
Hence, the domain is all real numbers except
−
1
and
3
Also written as
D
f
=
(
−
∞
,
−
1
)
∪
(
−
1
,
3
)
∪
(
3
,
+
∞
)
Equate the denominator(
x
2
−
2
x
−
3
) to zero, then solve the equation for
x
→
x
2
−
2
x
−
3
=
0
→
x
=
−
(
−
2
)
±
√
(
−
2
)
2
−
4
⋅
(
1
)
⋅
(
−
3
)
2
⋅
1
→
x
=
1
±
2
⇒
x
=
−
1
and
x
=
3
This means that, when
x
=
−
1
or
3
, we have the
x
2
−
2
x
−
3
=
0
Implying that
f
(
x
)
=
x
0
which is undefined.
Hence, the domain is all real numbers except
−
1
and
3
Also written as
D
f
=
(
−
∞
,
−
1
)
∪
(
−
1
,
3
)
∪
(
3
,
+
∞
)