If $f(x)=5x-12$, find a value for $x$ so that $f^{-1}(x)=f(x+1)$.
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
If $f(x)=5x-12$, find a value for $x$ so that $f^{-1}(x)=f(x+1)$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
\frac{47}{24}
If $f(x)=5x-12$, find a value for $x$ so that $f^{-1}(x)=f(x+1)$.
train