Answered

Discover the best answers at Westonci.ca, where experts share their insights and knowledge with you. Get immediate and reliable solutions to your questions from a community of experienced experts on our Q&A platform. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.

f(x)=23x+27 
g(x)=12x-d 

If (f^-1(g^-1(x)))= (g^-1(f^-1(x))), find d. 

How do I do this please?

Sagot :

konrad509
[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]
Thanks for using our platform. We're always here to provide accurate and up-to-date answers to all your queries. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.