Question

What is the domain of the function shown below r(x)=x/x^2-9

Answer 1

if you solve the denominator for 0, what do you get for "x"?

Answer 2

\[\large r(x) = \frac{x}{x^2-9}\] our function has a denominator so there is a restriction
we can either factor \[\large x^2-9 \] due to difference of squares formula... or solve \[\large x^2-9=0\] for x. There should be 2 solutions.

Answer 3

(x:xnot equal to 3) ?

Answer 4

ummm we're missing another value for x

hint
\[\large x^2-9=0 \]
difference of squares formula
\[\large (x+3)(x-3)=0\]
now solve for x

Answer 5

(x: all real numbers)?

Answer 6

solve
x+3 = 0 and solve x-3=0

Answer 7

(x:xnot equal to -3) ?