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

B0aGlzIGlzIGxpZmUgdGhlIGZ1bmN0aW9uIG9mIGNvbnRlbnQuIFRoZSBmdW5jdGlvbiBpcyBldmVuIG9yIG9kZCBhbmQgd2UgZmluZCB5b3UgZGlkbid0IG5vdCBrbm93IGhvdyB0byBwcmVzYWRlLgo=In summary, the problem is to show if the function (x^2|x-1|)/(SQRT(x-1)^2) is even or odd. The attempt at a solution involved using incorrect
  • #1
Government$
87
1

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.
 
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  • #2
Government$ said:

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
 

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

1. What is the formula for determining if a number is even or odd?

The formula for determining if a number is even or odd is to divide the number by 2. If there is no remainder, the number is even. If there is a remainder of 1, the number is odd.

2. How do you determine if a polynomial expression is even or odd?

To determine if a polynomial expression is even or odd, substitute -x for x in the expression. If the resulting expression is the same as the original expression, it is even. If the resulting expression is the negative of the original expression, it is odd.

3. What is the difference between even and odd functions?

An even function is symmetric about the y-axis, meaning that f(x) = f(-x). An odd function is symmetric about the origin, meaning that f(-x) = -f(x). In other words, even functions are symmetric about the y-axis and odd functions are symmetric about the origin.

4. How do you determine if a radical expression is even or odd?

To determine if a radical expression is even or odd, simplify the expression and then follow the steps for determining if a polynomial expression is even or odd. If the simplified expression is even, the original expression is even. If the simplified expression is odd, the original expression is odd.

5. How do you determine if a rational expression is even or odd?

To determine if a rational expression is even or odd, simplify the expression and then follow the steps for determining if a polynomial expression is even or odd. If the simplified expression is even, the original expression is even. If the simplified expression is odd, the original expression is odd.

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