Let the function f be given by the equation f(x)=7x-6. Evaluate f^{-1}(1) without finding an equation for the function f^{-1}(x).

Step 1 ：Let the function \(f\) be given by the equation \(f(x)=7x-6\). We are asked to evaluate \(f^{-1}(1)\) without finding an equation for the function \(f^{-1}(x)\).

Step 2 ：To find the inverse of a function at a particular point without finding the equation for the inverse function, we can use the property that the function and its inverse are reflections of each other over the line \(y=x\). This means that if \((a, b)\) is a point on the graph of the function, then \((b, a)\) is a point on the graph of the inverse function.

Step 3 ：So, to find \(f^{-1}(1)\), we need to find a value of \(x\) such that \(f(x) = 1\).

Step 4 ：Solving the equation \(7x - 6 = 1\), we find that \(x = 1\). This means that the point \((1, 1)\) is on the graph of the function \(f\).

Step 5 ：Therefore, the point \((1, 1)\) is also on the graph of the inverse function \(f^{-1}\), which means that \(f^{-1}(1) = 1\).

Step 6 ：Final Answer: \(\boxed{1}\)