Question

Check whether the function is homogenous or not. If yes then find the degree of the function
$g\left(x\right)=x^2-8x^3$.

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

Answer 1

Answer: (A)

Not homogenous

Given function is $g\left(x\right)=x^2-8x^3$

To check its Homogenitiy, we find $g\left(kx\right)$ which gives,

$g\left(kx\right)={k^{2}x}^2-8k^3{x}^3$

Now,

$\frac{g\left(kx\right)}{g\left(x\right)}=\frac{k^2{x}^2-8k^3{x}^3}{x^2-8x^3}\ne k^n$ where $k>0$ and $n$ is an integer.

$\therefore$ this function is not homogenous.