Question

please, express the function f(x)=|x|+|x-2| without using the absolute value signs

Answer 1

f(x) = |x| + |x -2 |

| x | = x , when x > 0

= - x , when x < 0

| x - 2| = x- 2, when x - 2> 0 i.e x > 2

= - ( x -2 ) when x -2 < 0 i.e x < 2


So f(x) = x + x- 2 = 2x - 2 , when x > 0 and x > 2

= - x + x - 2 = - 2 , when x < 0 and x > 2

= x - x + 2 = 2 , when x >0 and x < 2

= - x - x + 2 = - 2x - 2 , when x < 0 and x < 2

So there are four choices to write them.

I hope this helps .

Thanks

Abhishek Sinha