How do you find the domain and range of $\frac{x - 2}{x^{2} - 16}$ $(x - 2 )/ (x^2- 16)$ ?

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Answer 1 · 2017-10-12T11:02:54

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

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

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]}

How do you find the domain and range of (x - 2 )/ (x^2- 16)x−2x2−16(x - 2 )/ (x^2- 16)?