We have: #f(x) = 4 x + 3# and #g(x) = - 7 x + 10#
First, let's evaluate #g circ f#:
#Rightarrow g circ f = g (f(x))#
#Rightarrow g circ f = g (4 x + 3)#
#Rightarrow g circ f = - 7 (4 x + 3) + 10#
#Rightarrow g circ f = - 28 x - 21 + 10#
#Rightarrow g circ f = - 28 x - 11#
Let's suppose #y = g circ f#.
We must now find the inverse of #y#:
#Rightarrow y = - 28 x - 11#
Interchanging variables:
#Rightarrow x = - 28 y - 11#
Let's solve for #y#:
#Rightarrow x + 11 = - 28 y#
#Rightarrow y = - frac(1)(28) (x + 11)#
#therefore (g circ f)^(- 1) = - frac(1)(28) (x + 11)#
