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.

Also Read : Types of Functions in Maths – Domain and Range

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.

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