# Implicit and Explicit Function – Definition and Example

Here you will learn what is implicit and explicit function with definition and examples.

Let’s begin –

## Implicit and Explicit Function

Definition : A function defined by an equation not solved for the dependent variable is called implicit function. e.g. the equations $$x^3 + y^3$$ = 1 and $$x^y$$ = $$y^x$$, defines y as an implicit function. If y has been expressed in terms of x alone then it is called an Explicit function.

Example : Which of the following function is implicit function ?

(A ) y = $$x^2 + e^x + 5\over \sqrt{1 – cos^{-1}x}$$

(B) y = $$x^2$$

(C) xy – sin(x + y) = 0

(D) y = $$x^2 log x\over sin x$$

Solution : xy – sin(x + y) = 0 is implicit function because it is not clearly expressed in terms of x.