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Finding the Domain of Simple Rational Functions

Module by: Pradnya Bhawalkar, Kim Johnston

Summary: Finding the domain of rational functions with no other complications such as roots/radicals.

For fractions, the denominator (the bottom) of the fraction cannot equal 00. Determine domain restrictions by setting the denominator equal to 00 and solving.
Example 1 
Find the domain of y=1x y1x
{x|x0}xx0
Problem 1
Find the domain of y=1x-5 y1x5
[ Click for Solution 1 ]
Solution 1
{x|x5}xx5 since x-50x50, x5x5
[ Hide Solution 1 ]
Problem 2
Find the domain of y=4x+3x-7 y 4 x 3 x 7
[ Click for Solution 2 ]
Solution 2
{x|x7}xx7 since x-70x70, x7x7
[ Hide Solution 2 ]
Problem 3
Find the domain of y=7x5-2x y7x52x
[ Click for Solution 3 ]
Solution 3
{x|x52}xx52 since 5-2x052x0, x52x52
[ Hide Solution 3 ]
Problem 4
Find the domain of y=2x-3x+7 y 2 x 3 x 7
[ Click for Solution 4 ]
Solution 4
{x|x3-7} x x 3 7 since x3 x 3 and x-7 x 7
[ Hide Solution 4 ]
Problem 5
Find the domain of y=7x2x2-7x+3 y 7 x 2 x 2 7 x 3
[ Click for Solution 5 ]
Solution 5
{x|x123} x x 12 3 since 2x2-7x+30 2 x 2 7 x 3 0 , 2x-1x-30 2x 1 x 3 0 , 2x-10 2x 1 0 and x-30 x 3 0 , x12 x 12 and x3 x 3
[ Hide Solution 5 ]
Problem 6
y=2x+1x+52 y 2 x 1 x 5 2 -1
[ Click for Solution 6 ]
Solution 6
{x|x-5} x x 5 since x+520 x5 2 0 , x+50 x5 0 , x-5 x 5
[ Hide Solution 6 ]
Problem 7
Find the domain of y=x+3x2+25 y x 3 x 2 25 -1
[ Click for Solution 7 ]
Solution 7
{x|x} x x since x2+250 x 2 25 0 , x2-25 x2 25 , x x
[ Hide Solution 7 ]
Problem 8
Find the domain of y=x-7x2+2 y x 7 x 2 2 -1
[ Click for Solution 8 ]
Solution 8
{x|x} x x since x2+20 x 2 2 0 , x2-2 x2 2 , x x
[ Hide Solution 8 ]
Problem 9
Find the domain of y=5|x-3| y 5 x3
[ Click for Solution 9 ]
Solution 9
{x|x3}xx3 since |x-3|0 x3 0 , x-30 x3 0 , x3 x 3
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Problem 10
Find the domain of y=4|x|-4 y 4 x 4
[ Click for Solution 10 ]
Solution 10
{x|x-44} x x 4 4 since |x|-40 x 4 0 , |x|4 x 4 , x-4 x -4 and x4 x 4
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