Find $f^{-1}(x)$ if $f(x)=\frac{2 x+5}{7}$

Step 1 ：Substitute \(f^{-1}(x)\) into the expression for \(f\) to get \(f(f^{-1}(x))=\frac{2f^{-1}(x)+5}{7}\)

Step 2 ：Since \(f(f^{-1}(x))=x\) for all \(x\) in the domain of \(f^{-1}\), we can write the equation as \(x=\frac{2f^{-1}(x)+5}{7}\)

Step 3 ：Solve for \(f^{-1}(x)\) to get \(f^{-1}(x) = \frac{7x-5}{2}\)

Step 4 ：So, the final answer is \(\boxed{f^{-1}(x) = \frac{7x-5}{2}}\)