Determine if Even or Odd: (x^2|x-1|)/(SQRT(x-1)^2)

[Government$]

Homework Statement

Show that function is even or odd:

(x^2|x-1|)/(SQRT(x-1)^2)

Homework Equations

The Attempt at a Solution

(-x^2|-x-1|)/(SQRT(-x-1)^2)

After this i don't know how to procede.

 

[Ray Vickson]

Homework Statement

Show that function is even or odd:

(x^2|x-1|)/(SQRT(x-1)^2)

Homework Equations

The Attempt at a Solution

(-x^2|-x-1|)/(SQRT(-x-1)^2)

After this i don't know how to procede.

You need to start by using brackets correctly, so you do not end up writing things that are false. First, I assume you mean sqrt[(x-1)^2], and not [sqrt(x-1)]^2 (which is more-or-less what is meant by what you wrote).

So, if f(x) = x^2 |x-1|/sqrt[(x-1)^2] we have f(-x) = (-x)^2 |-x-1|/sqrt[(-x-1)^2]. Notice that this is not equal to -x^2 |-x-1|/sqrt[(-x-1)^2], which is what you wrote.

Anyway, now you need to figure out whether or not you have f(x) = f(-x) or f(x) = -f(-x) for all x, or neither.

When you don't know what to do, try plotting the function; just looking at its graph will tell you a lot.

RGV