The function \(f(x) = 2x - 5\) is a linear function with a slope of 2 and a y-intercept of -5. To find the inverse, solve for \(x\) in terms of \(y\):

\(y = 2x - 5\)

\(y + 5 = 2x\)

\(x = \frac{y + 5}{2}\)

Thus, the inverse function is \(f^{-1}(x) = \frac{x + 5}{2}\).

Sketch the graph of \(y = 2x - 5\), which is a straight line with a slope of 2 and y-intercept at -5.

Sketch the graph of \(y = \frac{x + 5}{2}\), which is a straight line with a slope of \(\frac{1}{2}\) and y-intercept at \(\frac{5}{2}\).

The graphs of \(y = f(x)\) and \(y = f^{-1}(x)\) should be symmetric about the line \(y = x\).