Answered

Welcome to Westonci.ca, the place where your questions find answers from a community of knowledgeable experts. Explore a wealth of knowledge from professionals across different disciplines on our comprehensive platform. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.

Consider the function f(x)=|-x-3/2|-1
and
The piecewise functions that coincide with the given function are

Consider The Function Fxx321 And The Piecewise Functions That Coincide With The Given Function Are class=

Sagot :

LammettHash

Recall the definition of absolute value,

[tex]|x| = \begin{cases}x&\text{if }x\ge0\\-x&\text{if }x<0\end{cases}[/tex]

• If (-x - 3)/2 ≥ 0, then |(-x - 3)/2| = (-x - 3)/2. So

f(x) = (-x - 3)/2 - 1 = (-x - 5)/2

Simplifying the condition gives

(-x - 3)/2 ≥ 0   ⇒   -x - 3 ≥ 0   ⇒   x ≤ -3

• Otherwise, if (-x - 3)/2 < 0, then |(-x - 3)/2| = -(-x - 3)/2, and we have

f(x) = -(-x - 3)/2 - 1 = (x + 3)/2 - 1 = (x + 1)/2

and

(-x - 3)/2 < 0   ⇒   -x - 3 < 0   ⇒   x > -3

So, as a piecewise function, we can write

[tex]f(x) = \left|\dfrac{-x-3}2\right| - 1 = \begin{cases}\dfrac{-x-5}2&\text{if }x\le-3\\\\\dfrac{x+1}2&\text{if }x>-3\end{cases}[/tex]

The piecewise functions that coincide with the given function is

f(x) = [tex]\frac{-(x+3)}{2} -1[/tex]  , where x is greater than or equal to -3

What is piecewise function?

A piecewise-defined function is a function defined by multiple sub-functions, where each sub-function applies to a different interval in the domain. Piecewise definition is actually a way of expressing the function, rather than a characteristic of the function itself.

According to the question

f(x) = [tex]|\frac{-x-3}{2} |-1[/tex]

The piecewise functions are :

f(x) = [tex]\frac{-(x+3)}{2} -1[/tex]

Case 1:

when x  ≥ -3  

F(x) = [tex]\frac{-(x+3)}{2} -1[/tex]

Case2:

when x  < -3  

F(x) = [tex]\frac{(x+3)}{2} -1[/tex]

Hence, The piecewise functions that coincide with the given function is

f(x) = [tex]\frac{-(x+3)}{2} -1[/tex]  , where x is greater than or equal to -3

To know more about piecewise function here:

https://brainly.com/question/12561612

#SPJ2

Thanks for using our platform. We're always here to provide accurate and up-to-date answers to all your queries. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.