meredith48034
Answered

NO LINKS!!
Find the function value, if possible. (If the answer is undefined, enter UNDEFINED.)
f(x) = |x|/x

a. f(x -1)
{ _____ if x < _____
{ _____ if x > _____



Answer :

mhanifa

Answer:

  • [tex]f(x - 1) = \left \{ {{-1 \ if \ x < 1} \atop {1 \ if \ x > 1}} \right.[/tex]

-----------------------------------

Given function:

  • f(x) = |x|/x

The function f(x - 1) is:

  • f(x - 1) =  |x - 1|/(x - 1)

The absolute value is always positive in this case and can't be zero otherwise it is undefined.

When x - 1 > 0, both the numerator and denominator are positive with same value so:

  • f(x - 1) = 1 if x - 1 > 0 or x > 1

When x - 1 < 0, the numerator is positive and denominator is negative with same value so:

  • f(x - 1) = - 1 if x - 1 < 0 or x < 1

semsee45

Answer:

[tex]f(x-1) \begin{cases}-1\;\; \text{if}\;\;x < 1\\\;\:\:1\;\; \text{if}\;\;x > 1\end{cases}[/tex]

Step-by-step explanation:

Given function:

[tex]f(x)=\dfrac{|x|}{x}[/tex]

Therefore:

[tex]f(x-1)=\dfrac{|x-1|}{x-1}[/tex]

The function is undefined when the denominator is zero.

Therefore, the function is undefined when x = 1.

As the numerator is an absolute value it is always positive.

[tex]\textsf{When}\;\;x < 1 \implies f(-x-1)=\dfrac{|-x-1|}{-x-1}=\dfrac{|-(x+1)|}{-(x+1)}=\dfrac{|x+1|}{-(x+1)}=-1[/tex]

[tex]\textsf{When}\;\;x > 1 \implies f(x-1)=\dfrac{|x-1|}{x-1}=1[/tex]

Other Questions