Given the functions #g(x) = 3/(x - 1)#, #f(x) = (x - 1)/(x - 3)# what is g(f(x))?

1 Answer
Dec 11, 2015

#(3x-9)/2#

Explanation:

To find #g(f(x))#, take #f(x)#, or #color(blue)((x-1)/(x-3))#, and plug it in for #x# in #g(x)#, or #3/(color(blue)(x)-3)#.

You get that

#g(f(x))=3/(color(blue)((x-1)/(x-3))-1)#

Multiply everything by #x-3#.

#=3/((x-1)/(x-3)-1)((x-3)/(x-3))=(3(x-3))/((x-1)-1(x-3))#

#=(3(x-3))/(x-1-x+3)=(3x-9)/2#