How do I solve f (x) = |x-5|

Answer 1

f(x) = x-5 if x>5

or = -(x-5) = 5-x if x<5

The solution is always positive, f(x)>0

f(x) = the absolute value of x-5

= the difference between x and 5, but make it positive

f(4) = -(4-5)= 1

f(6) = 6-5 = 1

Whether x>5 or x<5, make the difference positive

Another way to look at it is

f(x) = the positive square root of (x-5)²

f(3) = +square root of (3-5)²

= + square root of (-2)²

= + square root of 4

= +2 only. not -2