Answer :
[tex]f(x)=23x+27\\
y=23x+27\\
23x=y-27\\
x=\frac{1}{23}y-\frac{27}{23}\\
f^{-1}(x)=\frac{1}{23}x-\frac{27}{23}\\\\
g(x)=12x-d\\
y=12x-d\\
12x=y+d\\
x=\frac{1}{12}y+\frac{1}{12}d\\
g^{-1}(x)=\frac{1}{12}x+\frac{1}{12}d\\\\
[/tex]
[tex]\frac{1}{23}(\frac{1}{12}x+\frac{1}{12}d)-\frac{27}{23}=\frac{1}{12}(\frac{1}{23}x-\frac{27}{23})+\frac{1}{12}d\\ \frac{1}{276}x+\frac{1}{276}d-\frac{27}{23}=\frac{1}{276}x-\frac{27}{276}+\frac{1}{12}d\\ \frac{1}{276}d-\frac{1}{12}d=-\frac{27}{276}+\frac{27}{23}=\\ \frac{1}{276}d-\frac{23}{276}d=-\frac{27}{276}+\frac{324}{276}=\\ -\frac{22}{276}d=\frac{297}{276}=\\ -22d=297\\ d=-\frac{297}{22} [/tex]
[tex]\frac{1}{23}(\frac{1}{12}x+\frac{1}{12}d)-\frac{27}{23}=\frac{1}{12}(\frac{1}{23}x-\frac{27}{23})+\frac{1}{12}d\\ \frac{1}{276}x+\frac{1}{276}d-\frac{27}{23}=\frac{1}{276}x-\frac{27}{276}+\frac{1}{12}d\\ \frac{1}{276}d-\frac{1}{12}d=-\frac{27}{276}+\frac{27}{23}=\\ \frac{1}{276}d-\frac{23}{276}d=-\frac{27}{276}+\frac{324}{276}=\\ -\frac{22}{276}d=\frac{297}{276}=\\ -22d=297\\ d=-\frac{297}{22} [/tex]
