SOLUTION: state the domain: f(x)= 5x-4/10x^3-6x^2

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Question 447166: state the domain: f(x)= 5x-4/10x^3-6x^2
Answer by htmentor(1343) About Me  (Show Source):
You can put this solution on YOUR website!
The domain of the function is all values for which the function is defined.
f%28x%29+=+%285x-4%29%2F%2810x%5E3-6x%5E2%29
The denominator can be factored as 2x%5E2%285x+-+3%29
So f%28x%29+=+%285x-4%29%2F%282x%5E2%285x-3%29%29
The function is undefined where the denominator equals zero.
x = 0 and x = 3/5
So the domain is (-infinity,0) U (0,3/5) U (3/5,infinity)
The graph is below:
graph%28400%2C400%2C-10%2C10%2C-10%2C10%2C%285x-4%29%2F%2810x%5E3-6x%5E2%29%29