# Thread: Solve f(x) = 0

1. ## Solve f(x) = 0

I have a Piecewise function, that looks like,

-x , for x < - 1
4- X^2 , for -1 < X < 2
SQRT X-2 -1 , 2 < X < 11

Solve f (x) = 0

I am having troubles find where to start.
Do I want to plug in and solve = 0 to each equation?

2. ## Re: Solve f(x) = 0

try sketching the piece-wise function first ...

btw, this problem should be in the precalculus forum ... it's not advanced algebra.

3. ## Re: Solve f(x) = 0

Originally Posted by wolfwood
Do I want to plug in and solve = 0 to each equation?
That's certainly one way to do it - although you'd then need to check that any x value you found that makes f zero is in that part of the domain.

To get you started:
Does f(x) = 0 have a solution on the interval x<-1? (That's the interval $(-\infty, -1)$.)
Solve f(x)=0 on the interval x<-1.
So solve -x=0 on the interval x<-1.
That equation has one solution, x=0, but x=0 isn't in that interval (x<-1, the interval $(-\infty, -1)$ ).
Therefore f(x) = 0 has no solutions on the interval x<-1 ( the interval $(-\infty, -1)$ ).

4. ## Re: Solve f(x) = 0

Update: Exclusions removed

5. ## Re: Solve f(x) = 0

Originally Posted by MaxJasper
Careful there with the or equal to part of the inequality

You forgot the "holes" in the graph. Note that one of them is at x=2, so it cannot be a zero!

6. ## Re: Solve f(x) = 0

Originally Posted by johnsomeone
That's certainly one way to do it - although you'd then need to check that any x value you found that makes f zero is in that part of the domain.

To get you started:
Does f(x) = 0 have a solution on the interval x<-1? (That's the interval $(-\infty, -1)$.)
Solve f(x)=0 on the interval x<-1.
So solve -x=0 on the interval x<-1.
That equation has one solution, x=0, but x=0 isn't in that interval (x<-1, the interval $(-\infty, -1)$ ).
Therefore f(x) = 0 has no solutions on the interval x<-1 ( the interval $(-\infty, -1)$ ).
So for the next equation I got X = -2, or X = 2. X can not equal -2 since it is not agree with the interval, but X can equal 2. Am I getting the right idea?

7. ## Re: Solve f(x) = 0

Does it mean x=2 is not a root?

Update: thanks, exclusions removed.

8. ## Re: Solve f(x) = 0

Originally Posted by MaxJasper
Does it mean x=2 is not a root?

Update: thanks, exclusions removed.
x = 2 is not in the function's domain

9. ## Re: Solve f(x) = 0

It was X = Sqrt(4), but i simplified it to X = 2 or x = -2

10. ## Re: Solve f(x) = 0

Originally Posted by wolfwood
So for the next equation I got X = -2, or X = 2. X can not equal -2 since it is not agree with the interval, but X can equal 2. Am I getting the right idea?
Yes, that's the right idea, but I think you overlooked something here (as MaxJasper and skeeter pointed out).
The problem says f(x) = 4-x^2 when -1 < x < 2, but x=2 is not in that interval.