How do you show that #f(x)=(x-1)/(x+5)# and #g(x)=-(5x+1)/(x-1)# are inverse functions algebraically and graphically?
1 Answer
See below.
Explanation:
Two functions
#=(-(5x+1)/(x-1) - (x-1)/(x-1))/(-(5x+1)/(x-1) + (5(x-1))/(x-1))#
#=((-5x-1-x+1)/(x-1))/((-5x-1+5x-5)/(x-1))#
#=(-5x-1-x+1)/(-5x-1+5x-5)#
#=(-6x)/-6#
#=x#
#=-((5x-5)/(x+5) + (x+5)/(x+5))/((x-1)/(x+5)-(x+5)/(x+5))#
#=-((5x-5+x+5)/(x+5))/((x-1-x-5)/(x+5))#
#=-(5x-5+x+5)/(x-1-x-5)#
#=-(6x)/(-6)#
#=x#
Since we have proved
In the graph below,
It's clear to see that