Question

Check whether the function is homogenous or not. If yes then find the degree of the function
$g\left(x\right)=4-x^2$.

• A. Homogenous with degree 2
• B. Not homogenous
• C. Homogenous with degree 4
• D. None of these

Answer 1

The correct option is B Not homogenous

Given function is $g\left(x\right)=4-x^2$

To check the Homogenity of the function we find $g\left(kx\right)$

$g\left(kx\right)=4-k^2{x}^2$

$\frac{g\left(kx\right)}{g\left(x\right)}=\frac{4-k^2{x}^2}{4-x^2}\ne k^n$

Where $k>0$and $n$ is an integer.

$\therefore$ The function is not homogenous.