How do you find the domain of #f(x)=(x-2)/(x+4) #?

1 Answer
Jul 12, 2015

Answer:

The only restriction on the domain comes from the #(x+4)# denominator, which cannot be zero.

So the domain is #RR# \ #{-4}#.

In interval notation: #(-oo, -4) uu (-4, oo)#

Explanation:

#(x - 2)# is well defined for all #x in RR#

#(x + 4)# is well defined for all #x in RR#

So #f(x) = (x-2)/(x+4)# is well defined,

except when the denominator #(x+4) = 0#,
which happens when #x = -4#.