SOLUTION: Find the domain of the function f(x)=x-2/x^2-x-20. How do I even begin to do this problem?

Question 31110: Find the domain of the function f(x)=x-2/x^2-x-20. How do I even begin to do this problem?
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
SEE THE FOLLOWING AND TRY
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Graphs/30529: Obtain the domain and range for the following equation:
y= 3x-7/2x+8
1 solutions
Answer 17160 by venugopalramana(1167) About Me on 2006-03-16 23:39:56 (Show Source):
IS IT ...y= (3x-7)/(2x+8)....PLEASE PUT BRACKETS TO MAKE IT CLEAR....AS YOU PUT IT ,IT MAY MEAN
1...y= (3x)-7/(2x)+8...OR
2...y= (3x)-(7/2)x+ 8....OR
3...y= (3x) - 7/(2x) + 8........ETC.....
GOING BY y= (3x-7)/(2x+8)....SINCE DIVISION BY ZERO IS PROHIBITED IN MATHS...DOMAIN IS RESTRICTED BY 2X+8=0 OR X=-4...SO ALL VALUES OF X
EXCEPT X=-4 IS THE DOMAIN.....
FOR THIS DOMAIN WE FIND THAT AS X TENDS TO INFINITY...
Y TENDS TO 3/2...SINCE
y= (3x-7)/(2x+8) = {3-(7/X)}/{2+8/X)}...AS X TENDS TO INFINITY ....
Y= (3-0)/(2+0)=3/2
SO RANGE IS 3/2 TO INFINITY AS X VARIES FROM - INFINITY TO -4 AND
3/2 TO -INFINITY AS X VARIES FROM -4 TO INFINITY.
SEE GRAPH BELOW TO UNDERSTAND
graph( 600, 600, -50, 50, -5, 5, (3x-7)/(2x+8))

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Functions/30706: find all real numbers excluded from the domain of
{ { { f(x)= 16x^2-9/20x^2-23x+6 } } }
then give the domain using set notation.
1 solutions
Answer 17459 by venugopalramana(1167) About Me on 2006-03-19 22:35:18 (Show Source):
find all real numbers excluded from the domain of
{ { { f(x)= 16x^2-9/20x^2-23x+6 } } }
then give the domain using set notation.
f(x)= 16x^2-9/20x^2-23x+6
={(4X)^2-(3)^2}/{20X^2-8X-15X+6}
=(4X-3)^2/{4X(5X-2)-3(5X-2)}
=(4X-3)^2/(4X-3)(5X-2)
HENCE THE DOMAIN IS ALL REAL NUMBERS EXCEPT 4X-3=0..OR...4X=3...OR..X=3/4 AND
5X-2=0...OR....5X=2...OR....X=2/5.......
HENCE DOMAIN OF F(X)={X E R (X IS NOT EQUAL TO 3/4 AND 2/5)}
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