# Find the exponent of a function

I want to find the highest exponent of a function. Here is my code:

T22 = -x - x^5;
T23 = x^2 + x^6 - x^8;
V[n_] := (x^(3 n - 8) + (-1)^(n - 1) x^(n - 4))/(x + x^-1) T23 + (
x^(3 n - 7) + (-1)^(n - 2) x^(n - 1))/(x + x^-1) T22;


Now I want the the highest exponent of V[4], then I input the code:

Exponent[V[4],x]


The output is $12$. It's not the right answer. The right answer is $11$. I have not figured out why the output is not 11. Thank you!

Thank Jose for the previous problem. Now I make a replacement:

a = V[4] /. x -> (E - 1)/2 y + (E + 1)/2;
Exponent[FullSimplify@a, y]


Still, the output is 12, not 11. Since the replcement is a linear transformation, the highest exponent of $a$ should not change. Again, thanks.

• You should simplify V[n] first. This works Exponent[Simplify@V[4],x] – José Antonio Díaz Navas Dec 19 '17 at 14:19
• It works,thank you. – Leonard Dec 19 '17 at 14:24
• @JoséAntonioDíazNavas Turn your comment into a simple answer. – halirutan Dec 19 '17 at 14:53

Simplify first V[n] :
Exponent[Simplify@V[4],x]

• So the function should be simplified at first, then simplify the $V[n]$ for the specific number $n$. I should simplify each expression for each step, right? thanks again. – Leonard Dec 20 '17 at 1:37