How do you solve this? y=|x-1|+2 I know the domain and range .

Question

I need to solve my equation will absolute value functions. I need step by step instructions.

Answer 1

The absolute value equation |a x + b | = c (c ≥ 0) can be solved by rewriting as two linear equations

a x + b = c or a x + b = - c

y = | x - 1 | + 2

| x - 1 | = y  - 2

Let assume that (y - 2)  ≥ 0.

 x - 1 = y - 2       or    x - 1  = - ( y  - 2 )

 x  - y  + 1 = 0     or    x - 1 + y  - 2 = 0

 x  - y  + 1= 0      or    x + y - 3 = 0

 x  - y  + 1= 0 ------> (1)

x + y - 3 = 0 ------> (2)

Adding (1) & (2) equations.

(x  - y  + 1) + ( x + y - 3 ) = 0 + 0.

2 x - 2 = 0

2 x = 2

x = 1.

Substitute the x value in eq (1).

x  - y  + 1= 0

1 - y + 1 = 0

2 - y = 0

y = 2.

Therefore x = 1 and  y = 2.