MEDAL!!!! Algebra 1 help...

Let f and g be the functions given by f(x) = x^2 and g(x) = x|x|.

a. Is there a value of x, such that f(x) + g(x) = -100 ? If so, find x. If not, explain why no such value exists.

Question

MEDAL!!!! Algebra 1 help...


Let f and g be the functions given by f(x) = x^2 and g(x) = x|x|. 

a. Is there a value of x, such that f(x) + g(x) = -100 ? If so, find x. If not, explain why no such value exists.

calculusxy · Answer

@agent0smith

agent0smith · Answer

So basically$$\large x^2 + x \left| x \right|=-100$$

calculusxy · Answer

Yes...

calculusxy · Answer

But how would I solve for x?

agent0smith · Answer

Well clearly x would have to be negative, that way the x|x| would be negative.

But the x^2 will always have same value, since x|x| is really equivalent to -x^2, if x is negative.

So your equation, when x is negative, really is

$$\large x^2 - x^2 = -100$$

calculusxy · Answer

So this isn't possible. Right?

agent0smith · Answer

And if x was positive, the equation is

$$\large x^2 + x^2 = -100$$

calculusxy · Answer

The next one is the same thing, but it's now asking if there's a value that will equal to 50.

calculusxy · Answer

So how would I determine whether to have x|x| as a negative or a positive?

agent0smith · Answer

You should be able to figure it out, go through everything i said again

agent0smith · Answer

I gave two versions of the equation...