Determine the domain of the rational function Enter your ans

Determine the domain of the rational function. (Enter your answer using interval notation.) F(x) = 7x^2/x^2 - 3

Solution

f(x) = { 7x^2 } / x^2 - 3

to find the domain of the function set denominator to 0

x^2 - 3 = 0

add 3 on both sides

x^2 = 3

x = + - sqrt 3

therefore domain is all values of x except + - sqrt 3

interval notation

( - infinity , - sqrt 3 ) U ( - sqrt 3 , + sqrt 3 ) U ( sqrt 3 , + infinity )