Find the domain of the function fxx47x333x210x25 Write answe

Find the domain of the function f(x)=(x^4-7x^3+3)/(3x^2-10x-25). Write answer in set notation.

A rational function is undefined if the denominator is equals to 0. So let us first find where the denominator is 0.

hence

3x^2-10x-25 =0

=> 3x^2 -15x+5x -25 =0

=> 3x(x-5) +5(x-5)

=> (3x+5) (x-5)=0

=> x = -5/3 , 5

In order to the given rational function to be defined x should not be equal to 5 and -5/3

hence domain is in set notation:-

{ x element R : x!= 5/3 and x! = 5}