Determine the domain and range of the function y sin xx2 x

Determine the domain and range of the function y = sin x/x^2 -x - 6.

Solution

y = sin x / ( x^2 - x - 6 )

domain is all values of x where function exists

setting the denominator equal to zero

x^2 - x - 6 = 0

( x - 3 ) ( x+2 ) = 0

x = 3 , x = -2

domain is all values of x except x = 3 and -2

interval notation is ( -infinity , -2 ) U( -2 , 3 ) U ( 3 , + infinity )

range is all y values where the function exists

so range of the function is (-infinity , + infinity )