Inverse of a Function

To define the inverse of a function f i.e. f⁻¹ (f inverse), the function f must be one-to-one and onto.

For the inverse function f⁻¹, the co-domain of f becomes domain of f⁻¹.

If f : A → B then f⁻¹ : B → A

To get the graph of the inverse function, interchange the co-ordinates and plot the points.

Definition

Let f : A → B be a function. If there exists a function g : B → A such that (fog) = I_B and (gof) = I_A, then g is called the inverse of f. The inverse of f is denoted by f⁻¹.

Properties

The domain and the co-domain of both f and g are same then the above condition can be written as fog = gof = I.

If f⁻¹ exists then f is said to be invertible.

fof⁻¹ = f⁻¹of = I