What is the domain for √(3x-3)? * all real numbers except x=1
all real numbers for x≥1
all real numbers for x≥0
all real numbers except x=0

Domain and range are both
R
Explanation:
Note that your equation describes a line, since it is a polynomial of first degree. As a general result, every non-constant line has domain
R
and range
R
as well.
The domain is
R
because a line is, in particular, a polynomial, and every polynomial can be computed for every
x
.
The range is
R
because a non-constant line is either always growing or decreasing at a constant rate.
This means that, for every line, you always have one of this two situations:
lim
x
→
−
∞

f
(
x
)
=
−
∞
,

lim
x
→
∞

f
(
x
)
=
∞
or
lim
x
→
−
∞

f
(
x
)
=
∞
,

lim
x
→
∞

f
(
x
)
=
−
∞
and since every polynomial is continuous, it spans all the possible values from its minimum to its maximum. In other words, every line spans all the possible values from
−
∞
to
∞
, which means all the real number, thus the range is
R
.

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