How do I solve this equation/function?

Question

I'm not sure how to solve this:

Let the function f be defined by f(x) = x^2 - x. Which of the following has a negative value?
(a) f(-1)
(b) f(-1/2)
(c) f(0)
(d) f(1/2)
(e) f(1)

If anyone could EXPLAIN this--many thanks!! (I don't want the answer. Just a little help in understanding this, please.)

Answer 1

When you square a negative it becomes a positive because a negative times a negative is a positive. When you subtract a negative the same is true. Ex. -(-1) is really + 1. So a negative for x will always be a positive answer in this equation. That leaves out 2 of your choices.
Plug in the other 3 to find if -x is larger than x^2 giving you a negative answer. I think you'll find that d is the only answer.

Answer 2

OK, All you have to do is write out each function (a through e), substituting the amount inside the parentheses for x in the equation given in the first sentence.

a. f(-1)

f (-1) = (-1)^2 - (-1)
Now you have to solve it like this:
f (-1) = 1-(-1), so
f (-1) = 1+1 =2.
Since 2 is not a negative number, you have to try another one of the functions (b, c, d, or e).

I suggest you start at the bottom. Let me know if you can't figure it out.

Answer 3

You need to plug in the various options into the function to see which one of them gives you a negative number.

For example, if one of the solutions was F(5), then you would go through and replace each "x" with a 5 and see what the answer is. f(5)=5^2-5

Five squared is 25, so 25-5 equals 20. Try out the various numbers for each function and see which one gives you the right answer. Remember that when negative numbers are multiplied together, the result is positive.

Answer 4

answer is D

if you plug 1/2 into the equation, the following will happen:

if you square 1/2, it turns to 1/4. so the whole equation will be 1/4-1/2, which is a negative answer

Answer 5

Just substitute the number in parentheses for x. For example, c is not the answer, because f(0) = 0^2 - 0 = 0.

Answer 6

All you have to do is plug the number in for x...
So for (a)... (-1)^2 -(1)=1+1= 2
Which ever one gives you a negative value... is the correct answer...

Answer 7

Think of it as y = x^2 - x.

This is asking, "for what value of x is y less than zero?"

Your multiple choice answers are giving you values of x (inside the parentheses), so simply solve the equation for each value of x.

Hope this helps!

Answer 8

you plug every number for x. example: f(-1)= (-1)^2-(-1)=0, meaning you have to plug other numbers and see if they work.