Suppose the two functions are as follow:
\(\begin{array}{c}f\left( x \right) = x + 73\\g\left( x \right) = x - 73\end{array}\)
Now, find\(f \circ g\) as follow:
\(\begin{array}{c}\left( {f \circ g} \right)\left( x \right) = f\left( {g\left( x \right)} \right)\\ = f\left( {x - 73} \right)\\ = \left( {x - 73} \right) + 73\\ = x\end{array}\)
Now, find \(g \circ f\) as follow:
\(\begin{array}{c}\left( {g \circ f} \right)\left( x \right) = g\left( {f\left( x \right)} \right)\\ = g\left( {x + 73} \right)\\ = \left( {x + 73} \right) - 73\\ = x\end{array}\)
From above, it can see that,
\(\left( {f \circ g} \right)\left( x \right) = \left( {g \circ f} \right)\left( x \right)\)
Therefore, the functions\(f\left( x \right) = x + 73\) and \(g\left( x \right) = x - 73\) are inverse function,
\(\begin{array}{c}f\left( x \right) = x + 73\\g\left( x \right) = x - 73\end{array}\)
Now, find\(f \circ g\) as follow:
\(\begin{array}{c}\left( {f \circ g} \right)\left( x \right) = f\left( {g\left( x \right)} \right)\\ = f\left( {x - 73} \right)\\ = \left( {x - 73} \right) + 73\\ = x\end{array}\)
Now, find \(g \circ f\) as follow:
\(\begin{array}{c}\left( {g \circ f} \right)\left( x \right) = g\left( {f\left( x \right)} \right)\\ = g\left( {x + 73} \right)\\ = \left( {x + 73} \right) - 73\\ = x\end{array}\)
From above, it can see that,
\(\left( {f \circ g} \right)\left( x \right) = \left( {g \circ f} \right)\left( x \right)\)
Therefore, the functions\(f\left( x \right) = x + 73\) and \(g\left( x \right) = x - 73\) are inverse function,