MHB Absolute Value with two expressions.

AI Thread Summary
To solve the absolute value problem, the expression is defined as a piecewise function with three segments. The only solution found so far is at x=1, but there should be two valid roots within the specified domains. To sketch the area between -1 and 2, calculate the endpoints of the middle segment, which are f(-1) = -2 and f(2) = 1. Plot the points (-1, -2) and (2, 1), then connect them with a line segment to complete the graph. Understanding the roots and their respective domains is crucial for accurate representation.
stuart4512
Messages
3
Reaction score
0
How do I do this? I have tried a few methods and end up getting x values that don't work when placed back into the equation.

View attachment 3670
 

Attachments

  • Untitled.png
    Untitled.png
    3.4 KB · Views: 86
Mathematics news on Phys.org
I would write the expression as a piecewise function:

$$f(x)=\begin{cases}-3x-5, & x<-1 \\[3pt] x-1, & -1\le x\le2 \\[3pt] 3x-5, & 2<x \\ \end{cases}$$

Can you proceed?

edit: I have moved this thread here from our Linear Algebra subforum, as this is a better fit. :D
 
I got the only solution to be at x=1.
How do I sketch the area between -1 and 2?
 
stuart4512 said:
I got the only solution to be at x=1.
How do I sketch the area between -1 and 2?

You should find 2 valid roots. Check the root of each piece, and if it is in the given domain for that piece, then it is a valid root.

As for the middle piece, just compute the end points, and connect them with a line segment.

$$f(-1)=-2$$

$$f(2)=1$$

So, plot the points $(-1,-2),\,(2,1)$ and connect them.
 
Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
Back
Top