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.
