What is "if and are inverse functions of each other and?

If ( f ) and ( g ) are inverse functions of each other, it means that when ( f ) takes an input ( x ) and produces an output ( y ), ( g ) can take ( y ) as input and produce ( x ) as output. In other words, if ( f(x) = y ), then ( g(y) = x ).

This relationship implies that the composition of the two functions, ( f(g(x)) ) and ( g(f(x)) ), will return the input ( x ) for any value of ( x ).

If the functions ( f ) and ( g ) are inverses, they are said to "undo" each other. This means that applying both functions in succession will result in the identity function, ( f(g(x)) = g(f(x)) = x ).

When two functions are inverses of each other, they mirror each other across the line ( y = x ) on a graph. This means that if you were to graph ( f ), then reflect it across the line ( y = x ), you will end up with the graph of ( g ) and vice versa.