What is Homogeneous Function – Definition and Example

Here you will learn what is homogeneous function definition with example.

Let’s begin –

What is Homogeneous Function ?

Definition : A function is said to be homogeneous with respect to any set of variables when each of its terms is of the same degree with respect to those of the variables.

For example, \(5x^2 + 3y^2 – xy\) is homogeneous in x and y.

Symbolically if, f(tx,ty) = \(t^n\)f(x, y) then f(x, y) is homogeneous function of degree n.

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

Example : Which of the following function is not homogenous ?

(i)  \(x^3 + 8x^2y + 7y^3\)

(ii)  \(y^2 + x^2 + 5xy\)

(iii)  \(xy\over x^2 + y^2\)

(iv)  \(2x – y + 1\over 2y – x + 1\)

Solution : \(2x – y + 1\over 2y – x + 1\) is not homogenous because it does not have the same degree in each term.

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