For fractions, the denominator (the bottom) of the fraction cannot equal 00. Determine domain restrictions by setting the denominator equal to 00 and solving.
Find the domain of y=1x
y1x
{x|x≠0}xx0
Find the domain of y=1x−5
y1x5
{x|x≠5}xx5 since x−5≠0x50, x≠5x5
Find the domain of
y=4x+3x−7
y
4
x
3
x
7
{x|x≠7}xx7 since x−7≠0x70, x≠7x7
Find the domain of
y=7x5−2x
y7x52x
{x|x≠52}xx52 since 5−2x≠052x0, x≠52x52
Find the domain of
y=2x−3x+7
y
2
x
3
x
7
{x|x≠3∨-7}
x
x
3
7
since
x≠3
x
3
and
x≠-7
x
7
Find the domain of
y=7x2x2−7x+3
y
7
x
2
x
2
7
x
3
{x|x≠12∨3}
x
x
12
3
since
2x2−7x+3≠0
2
x
2
7
x
3
0
,
2x−1x−3≠0
2x
1
x
3
0
,
2x−1≠0
2x
1
0
and
x−3≠0
x
3
0
,
x≠12
x
12
and
x≠3
x
3
y=2x+1x+52
y
2
x
1
x
5
2
-1
{x|x≠-5}
x
x
5
since
x+52≠0
x5
2
0
,
x+5≠0
x5
0
,
x≠-5
x
5
Find the domain of
y=x+3x2+25
y
x
3
x
2
25
-1
{x|x∈ℝ}
x
x
since
x2+25≠0
x
2
25
0
,
x2≠-25
x2
25
,
x∈ℝ
x
Find the domain of
y=x−7x2+2
y
x
7
x
2
2
-1
{x|x∈ℝ}
x
x
since
x2+2≠0
x
2
2
0
,
x2≠-2
x2
2
,
x∈ℝ
x
Find the domain of
y=5|x−3|
y
5
x3
{x|x≠3}xx3
since
|x−3|≠0
x3
0
,
x−3≠0
x3
0
,
x≠3
x
3
Find the domain of
y=4|x|−4
y
4
x
4
{x|x≠-4∨4}
x
x
4
4
since
|x|−4≠0
x
4
0
,
|x|≠4
x
4
,
x≠-4
x
-4
and
x≠4
x
4
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