Asked by Olivia
what are the domains of y=ln(x^2-4x)
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Answered by
MathMate
The domain of y=f(x) is the range of values of x such that f(x) exists.
We know that the ln() function does not admit negative arguments, so the domain of f(x) consist of the ranges of x which makes x^2-4x non-negative, or
x^2-4x≥0 .... (1)
The solution to equation (1) is the domain of f(x).
If you are not sure what to do, plot g(x)=x^2-4x and the parts of the curve that is above the x-axis correspond to the values of the domain. The domain in this case consists of two disjoint intervals.
We know that the ln() function does not admit negative arguments, so the domain of f(x) consist of the ranges of x which makes x^2-4x non-negative, or
x^2-4x≥0 .... (1)
The solution to equation (1) is the domain of f(x).
If you are not sure what to do, plot g(x)=x^2-4x and the parts of the curve that is above the x-axis correspond to the values of the domain. The domain in this case consists of two disjoint intervals.
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