Question 108978
Find the domain and range of the following functions.  Express your answer in interval notation.  
a) sqrt(x**2-3)   
Domain: 
Solve, x^2-3>=0
x^2 >= 3
x>=sqrt3 U x<=-sqrt3
Interval notation: (-inf,-sqrt(3))U(sqrt3,+inf)
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Range: 
Square roots are >=0 so the range is (0,+inf)
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b) two over x squared minus five x plus six
f(x) = (2/x^2-5x+6) 
Domain:
Solve x^2-5x+6 = 0  
(x-3)(x-2)=0
x = 3 or x=2
Domain is "All Real Numbers except x = 2 and x=3.
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Range:
{{{graph(400,300,-10,10,-40,40,2/(x^2-5x+6))}}}

(0,+inf)U(-inf,-8/11]
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Cheers,
Stan H.