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
xx≠0xx0
Find the domain of y=1x−5
y1x5
xx≠5xx5 since x−5≠0x50, x≠5x5
Find the domain of
y=4x+3x−7
y
4
x
3
x
7
xx≠7xx7 since x−7≠0x70, x≠7x7
Find the domain of
y=7x5−2x
y7x52x
xx≠52xx52 since 5−2x≠052x0, x≠52x52
Find the domain of
y=2(x−3)(x+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−1)(x−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+52-1
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+25-1
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+2-1
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
xx≠3xx3
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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