How do you find the domain of #f(x)= (8x)/((x-1)(x-2)) #?

2 Answers
Mar 30, 2018

Answer:

#x inRR,x!=1,2#

Explanation:

#f(x)" is defined for all values of x except values which"#
#"make f(x) undefined"#

#"the denominator of f(x) cannot be zero as this would make"#
#"f(x) undefined. Equating the denominator to zero and "#
#"solving gives the values that x cannot be"#

#"solve "(x-1)(x-2)=0#

#rArrx=1,x=2larrcolor(red)"are excluded values"#

#"domain is "x inRR,x!=1,2#

#(-oo,1)uu(2,+oo)larrcolor(blue)"in interval notation"#
graph{(8x)/((x-1)(x-2)) [-10, 10, -5, 5]}

Mar 30, 2018

Answer:

Ask yourself where the function is defined.

Explanation:

Since the given function is a rational function, look where is the denominator is equal to zero. (#(8x)/0 #is not defined)
(#x-1)(x-2)=0# if #x_1=1# or #x_2=2#
The domain of #f(x)# is : #RR-{1,2}# real number except 1 and 2