Find the domain of the given function. Write your answers in both set builder and interval notation, also with absolute value. : f(x)= 3x`/2x^3 -5x +3x`

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llltkl | College Teacher | (Level 3) Valedictorian

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`f(x)=(3x)/(2x^3-5x^2+3x)`

`rArr f(x)=(3x)/(x(2x^2-5x+3))`

Domain is "All Real Numbers" unless there is some reason for
it to be restricted.

Here, the restriction is division by zero.

The zeros of the denominator are `x=0,1,3/2`

f(x) is not defined at `x=0,1,3/2`

Hence, the domain of the function f(x) is `RR-{0,1,3/2}` or

`S={x|x in RR, x!=0,1,3/2}` where S is domain of f(x).

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