Find the domain of
A) f(x) = Squareroot (x^4 - x^2)
B) g(x)= Squareroot (x/x-1) + 1
A) f(x) = Squareroot (x^4 - x^2)
B) g(x)= Squareroot (x/x-1) + 1
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A) f(x) = sqrt(x^4 - x^2)
The domain means the function must be able to be evaluated, so since square root only is evaluated when the value is greater than or equal to 0, set up the equation:
x^4 - x^2 >= 0
Factor:
x^2(x^2 - 1) >=0
x^2(x + 1)(x - 1) >= 0
So, x^2 will ALWAYS be >=0, so it can be disregarded, leaving:
(x + 1)(x - 1) >=0
So, either both terms must be positive OR both terms must be negative, leaving:
x >=1 or x<= -1 as the solutions.
The domain is then (-infinity, -1] U [1, infinity)
Use a similar approach to try B yourself!
The domain means the function must be able to be evaluated, so since square root only is evaluated when the value is greater than or equal to 0, set up the equation:
x^4 - x^2 >= 0
Factor:
x^2(x^2 - 1) >=0
x^2(x + 1)(x - 1) >= 0
So, x^2 will ALWAYS be >=0, so it can be disregarded, leaving:
(x + 1)(x - 1) >=0
So, either both terms must be positive OR both terms must be negative, leaving:
x >=1 or x<= -1 as the solutions.
The domain is then (-infinity, -1] U [1, infinity)
Use a similar approach to try B yourself!