SOLUTION: Find the domain and range of the following functions. Express your answer in interval notation. a) sqrt(x**2-3) meaning the square root of x squared minus three b)2/x**2-5x+6

Algebra ->  Radicals -> SOLUTION: Find the domain and range of the following functions. Express your answer in interval notation. a) sqrt(x**2-3) meaning the square root of x squared minus three b)2/x**2-5x+6       Log On


   

Question 108978: Find the domain and range of the following functions. Express your answer in interval notation. a) sqrt(x**2-3) meaning the square root of x squared minus three b)2/x**2-5x+6 meaning two over x squared minus five x plus six
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
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%28400%2C300%2C-10%2C10%2C-40%2C40%2C2%2F%28x%5E2-5x%2B6%29%29
(0,+inf)U(-inf,-8/11]
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Cheers,
Stan H.