How do you solve and write the following in interval notation: #(4-x) /( x-8)>=0#?

1 Answer
Jan 21, 2017

Answer:

The answer is #x in [ 4, -8 [#

Explanation:

Let #f(x)=(4-x)/(x-8)#

The domain of #f(x)# is #D_f(x)=RR-{8}#

Let's build the sign chart

#color(white)(aaaa)##x##color(white)(aaaa)##-oo##color(white)(aaaa)##4##color(white)(aaaaaaaa)##8##color(white)(aaaaaaa)##+oo#

#color(white)(aaaa)##4-x##color(white)(aaaa)##+##color(white)(aaaa)##-##color(white)(aaaa)##color(red)(||)##color(white)(aaaa)##-#

#color(white)(aaaa)##x-8##color(white)(aaaa)##-##color(white)(aaaa)##-##color(white)(aaaa)##color(red)(||)##color(white)(aaaa)##+#

#color(white)(aaaa)##f(x)##color(white)(aaaaa)##-##color(white)(aaaa)##+##color(white)(aaaa)##color(red)(||)##color(white)(aaaa)##-#

Therefore,

#f(x>=0)# when #x in [ 4, -8 [#