Thread: 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?

try sketching the piece-wise function first ...


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

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 .)
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 ).
Therefore f(x) = 0 has no solutions on the interval x<-1 ( the interval ).

Update: Exclusions removed

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!

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 .)
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 ).
Therefore f(x) = 0 has no solutions on the interval x<-1 ( the interval ).

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?

Does it mean x=2 is not a root?

Update: thanks, exclusions removed.

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

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

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.

Oh yeah your right.