Question

if f(x) =||x|-1| graph of (x) will be​

Answer 1

Given :  f(x) = | |x|  - 1 |  

To find :  graph of f(x)

Solution:

f(x) = | |x|  - 1 |  

|x|  =  x   for  x ≥ 0

|x| =  -x   for  x < 0

Case  1     x  ≥ 0

| x - 1 |     = x - 1    if  x  ≥ 1

| x - 1 |    =  -(x - 1) = 1 -x  if  0 ≤ x  < 1

Case  1     x  <  0

| -x - 1 |   = x + 1     if       -1 <  x  < 0

| -x - 1 |   = -1 - x     if          x ≤  -1

f(x)  =     -1 - x      x ≤  -1

              x + 1     -1 <  x  < 0

              1 - x       0 ≤ x  < 1

              x - 1      x  ≥ 1

Graph shape would be  somewhat like W

Graph attached

x f(x) = | |x| - 1 |

-4 3

-3 2

-2 1

-1 0

-0.5 0.5

0 1

0.5 0.5

1 0

2 1

3 2

4 3

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