Question

Split the Function into piece wise defined one

f(x) = |x+1| + |x-3| + | | x+5| |

Answer 1

whats the last one?

Answer 2

it is modulus of modulud ||x+5|| ,

Answer 3

and defining the lines is simple enough ... that last one tho is pecular notation

Answer 4

Is that really a double modulus? If it is then the second modulus sign can be removed. i.e. \(||x+5|| = |x+5|\)

The crucial points where the function changes value will be at x=-5, -1, 3.

Also remember that \(|x-a| = \displaystyle \frac{(x-a) \;\;\;\; x \ge a}{-(x-a) \;\;\;\; x<a}\)

Sorry for poor formatting, too lazy to search for \(\LaTeX\) formatting of a matrix.

Answer 5

Yup its a Double Modulus....

Answer 6

f(x) = |x+1| + |x-3| + | | x+5| |



x = -inf to -1: (-x-1)+(-x+3)+(-last one)
x = -1 to 3 : (x+1)+(-x+3)+(-last one)
x = 3 to +inf : (x+1)+(x-3)+(last one)