Find the domain of the rational function.

Question

F(x)=3x(x-2)/6x^2-41x-7

Answer 1

To find the domain you need to solve the denominator for all values that would make it equal to zero:

 

so 6x²-41x-7=0

(6x+1)(x-7)=0

6x+1=0  and x-7=0

6x=-1

x=-1/6  and x=7

 

so the domain is x can be all real numbers except -1/6 and 7 because those would make the denominator equal to zero and you cannot divide by zero.