How do you compute (fog) and (gof) if #f(x) = (3x-1) / (2x+5)# and #g(x) =(7x+3) / (3x-1)#?

Question

Liam Brennan · Accepted Answer

undefined To compute (fog) and (gof), first find the compositions f(g(x)) and g(f(x)).

1. To find (fog), substitute g(x) into f(x). So, (fog)(x) = f(g(x)).
   (fog)(x) = f(g(x)) = f((7x+3)/(3x-1)) = [3(7x+3) - 1] / [2(7x+3) + 5]

2. To find (gof), substitute f(x) into g(x). So, (gof)(x) = g(f(x)).
   (gof)(x) = g(f(x)) = g((3x-1)/(2x+5)) = [7(3x-1) + 3] / [3(3x-1) - 1]

Serenity Jones · Answer

#(f o g)(x)=(18x+10)/(29x+1)#

#(g o f)(x)=(27x+8)/(7x-8)# Given: #f(x)=(3x-1)/(2x+5)# and #g(x)=(7x+3)/(3x-1)# Solution for #(f o g)(x)# #(f o g)(x)=f(g(x))=(3g(x)-1)/(2g(x)+5)=(3*((7x+3)/(3x-1))-1)/(2*((7x+3)/(3x-1))+5)# #(f o g)(x)=(21x+9-3x+1)/(14x+6+15x-5)=(18x+10)/(29x+1)# #(f o g)(x)=(18x+10)/(29x+1)# ~~~~~~~~~~~~~~~ Solution for #(g o f)(x)# #(g o f)(x)=g(f(x))=(7*f(x)+3)/(3*f(x)-1)=(7*(3x-1)/(2x+5)+3)/(3*(3x-1)/(2x+5)-1)# #(g o f)(x)=(21x-7+6x+15)/(9x-3-2x-5)=(27x+8)/(7x-8)# #(g o f)(x)=(27x+8)/(7x-8)# God bless....I hope the explanation is useful..