Question 447166
The domain of the function is all values for which the function is defined.
{{{f(x) = (5x-4)/(10x^3-6x^2)}}}
The denominator can be factored as {{{2x^2(5x - 3)}}}
So {{{f(x) = (5x-4)/(2x^2(5x-3))}}}
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(400,400,-10,10,-10,10,(5x-4)/(10x^3-6x^2))}}}