Hi all

quick question

given f(x)=(x-5)/X^2-5x+6 find range

EDIT

ok so i think i got it, let me know if this seems right

so write the

equation as y=(x-5)/(x^2-5x+6)

simplify y(x^2-5x+6)=(x-5)

range of y will be values where discriminant > or equal to 0

yx^2 - 5xy + 6y = x - 5

yx^2 - 5xy +6y - x + 5 = 0

quadratic is relative to x, where a = y, b = -(5y+1) and c = 6y+5

discriminant = b^2 - 4ac so

(-5y-1)^2 - 4y(6y+5)

25y^2 +5y +5y +1 - 24y^2 - 20y

y^2 -10y + 1 < or equal to 0

y^2 - 10y + 1 = 0

so range = (-infinty, 5-sqrt(24)] u [5+sqrt(24), infinity)

basically I understand HOW questions like this work, i do not however understand WHY they work. any insight is appreciated

EDIT

http://www.analyzemath.com/DomainRan..._rational.html
EDIT

Looking for more than just this is how you find range of rational functions lol

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