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Question 833415: Find the domain of the function.
(a) (2x+1)/(x^2+x-2)
(b) cube square of x/x^2+1
(c)(sqrt4-x)+(sqrtx^2 -1)
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Find the domain of the function.
(a) (2x+1)/(x^2+x-2)
Factor: (2x+1)/[(x+2)(x-1)
Domain: All Real Numbers except x = -2 and x = 1
Interval Notation: (-oo,-2]U(-2,1]U(1,+oo)
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(b) cbrt[x/x^2+1]
Domain: All Real Numbers
Interval Notation: (-oo,+oo)
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(c)(sqrt(4-x)+sqrt(x^2-1)
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= sqrt(4-x) + sqrt[(x+1)(x-1)]
Solve (x+1)(x-1) >= 0
x <= -1 or x >= 1
Interval Notation: (-oo,-1]U[1,+oo)
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Solve 4-x >= 0
x <= 4
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Domain: All Real Numbers x <=-1 or 1<= x <=4
Interval Notation: (-oo,-1]U[1,4]
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Cheers,
Stan H.
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