Question

Redefine the function: f(x) = |x – 1|- |x + 6]. Write its domain also.​

Answer 1

Given : f(x) = |x – 1|- |x + 6|

To Find : Redefine the function  

Find domain also.​

Solution:

f(x) = |x – 1|- |x + 6|

| y |  =  y  if y ≥ 0    

       - y  if y < 0

Case 1 :  x  ≥  1

=> | x - 1 |  = x - 1    and | x + 6 |   = x + 6

f(x) = x - 1 - ( x + 6 )

  =  -7      for x ≥  1

-6 ≤  x  <  1

|x + 6|   = x + 6  and     | x - 1 |  = -(x - 1)

f(x) = -(x - 1) - (x + 6)

  =  -2x - 5   for  -6 ≤  x  <  1

x  < - 6

|x + 6|   = -(x + 6)  and     | x - 1 |  = -(x - 1)

f(x) = -(x - 1) - (-(x + 6) )

   =    7   for x  < - 6

f(x)  =  7   for    < - 6

        -2x - 5  for  -6 ≤  x  <  1

         -7   for  x ≥ 1

Domain is  Real numbers

Range is  [-7 , 7]

Learn More:

If f(x) =||x|-1| graph of (x)

brainly.in/question/17509624

|x|+|x-1|+|x-2|+|x-3|=3k

brainly.in/question/17699726