# Find the domain of the function. Write your answer in both set builder and interval notation. f(x)= 8x / 2x^2 - x Find teh domain of `f(x)=(8x)/(2x^2-x)` :

The domain is the set of all possible inputs. Domain restrictions are typically division by zero, taking even roots of negative numbers, and taking logarithms of nonpositive numbers.

For this problem we are only concerned with division by zero.

The denonminator factors as x(2x-1)....

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Find teh domain of `f(x)=(8x)/(2x^2-x)` :

The domain is the set of all possible inputs. Domain restrictions are typically division by zero, taking even roots of negative numbers, and taking logarithms of nonpositive numbers.

For this problem we are only concerned with division by zero.

The denonminator factors as x(2x-1). By the zero product property the denominator will be zero if x=0 or 2x-1=0 ==> `x=1/2` . Thus these values cannot be in the domain.

As this is a rational function, all other values of x are permissable.

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The domain is `{x|x in RR,x!=0,1/2}` or `x in (-oo,0)uu(0,1/2)uu(1/2,oo)`

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