Suppose you are provided with a graph How can you determine

Suppose you are provided with a graph. How can you determine if there is an inverse of this function?

Solution

We know that if f and g are two functions such that f(g(x)) = x and g(f(x)) = x, then g is the inverse of f i.e. g = f^-1 and f is the inverse of g i.e. f = g^-1 .

If it is possible to reflect the graph of f(x) about the line y = x, then the inverse of the function ( whose graph is furnished) exists as the graph of f^-1 is the reflection about the line y = x of the graph of f.