How do you solve and write the following in interval notation: #x / (x-9) >= 0#?

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Answer 1 · 2017-01-18T17:41:37

The answer is # x in ] -oo, 0] uu ] 9,+ oo[ #

Let #f(x)=x/(x-9)#

The domain of #f(x)# is #D_f(x)=RR-{9}#

Let's do a sign chart

#color(white)(aaaa)##x##color(white)(aaaa)##-oo##color(white)(aaaa)##0##color(white)(aaaa)####color(white)(aaaa)##9##color(white)(aaaaa)##+oo#

#color(white)(aaaa)##x##color(white)(aaaaaaa)##-##color(white)(aaaaaa)##+##color(white)(a)####color(white)(a)##∥##color(white)(aa)##+#

#color(white)(aaaa)##x-9##color(white)(aaaa)##-##color(white)(aaaaaa)##-##color(white)(a)####color(white)(a)##∥##color(white)(aa)##+#

#color(white)(aaaa)##f(x)##color(white)(aaaaa)##+##color(white)(aaaaaa)##-##color(white)(a)####color(white)(a)##∥##color(white)(aa)##+#

Therefore,

#f(x)>=0# when # x in ] -oo, 0] uu ] 9,+ oo[ #