Answered

Get expert advice and community support for all your questions on IDNLearn.com. Our experts provide prompt and accurate answers to help you make informed decisions on any topic.

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 :

LammettHashidn

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

Thank you for contributing to our discussion. Don't forget to check back for new answers. Keep asking, answering, and sharing useful information. Your questions find clarity at IDNLearn.com. Thanks for stopping by, and come back for more dependable solutions.