How do you find the domain and range of $(x^2-64)/(x-8)$ ?

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Answer 1 · 2016-04-01T18:59:37

Domain: $RR "\" { 8 } = (-oo, 8) uu (8, oo)$

Range: $RR "\" { 16 } = (-oo, 16) uu (16, oo)$

$f(x) = (x^2-64)/(x-8) = ((x-8)(x+8))/(x-8) = x+8$

with exclusion $x != 8$

When $x=8$ , both the numerator and denominator are $0$ resulting in an undefined value. So $x=8$ is not in the domain.

$f(x)$ is well defined for all other values of $x$

So the domain is $RR "\" { 8 } = (-oo, 8) uu (8, oo)$

The range is the set of values that $f(x)$ takes for $x in RR "\" { 8 }$ , namely $(-oo, 16) uu (16, oo)$ .

Note that $f(x)$ can take any value except $16$

How do you find the domain and range of (x^2-64)/(x-8)(x^2-64)/(x-8)?