Question

How do you find the domain and range of `(x - 2 )/ (x^2- 16)`?

Answer 1

Domain : `x in RR | x != -4, x != 4` ,in interval notation , `(-oo, -4)uu(-4,4) uu(4,oo)`
Range : `f(x) in RR or (-oo , oo)`

Explanation:

`f(x)= (x-2)/(x^2-16) = (x-2)/((x+4)(x-4))` .

Domain (input `x`) : Denominator should not be zero ,otherwise

`f(x)` will be undefined `:.x+4 != 0 or x != -4` and

`x-4 != 0 or x != 4`, so `x` can be any real number except

`x=4 or x= -4`

Domain : `x in RR | x != -4, x != 4` or

in interval notation , `(-oo, -4)uu(-4,4) uu(4,oo)`

Range : `f(x)` can be any real number

Range : `f(x) in RR or (-oo , oo)`

graph{(x-2)/(x^2-16) [-10, 10, -5, 5]}