The given equation is in the form of an absolute value function. We know that an absolute value function can be rewritten as two separate linear functions, one for the positive and one for the negative case.
First, consider the inside of the absolute value function, |x+1|. There are two scenarios possible here.
1) x+1 is greater or equal to zero i.e. x is greater or equal to -1.
2) x+1 is less than zero i.e. x is less than -1.
Let's handle each case electively:
1) When x ≥ -1, replace |x+1| with (x+1), because when x is greater or equal to -1, (x+1) will be non-negative. Our equation becomes y = 14*(x+1) + 2. Simplifying, we get y = 14x + 16, so f(x) = 14x + 16 with a domain x ≥ -1.
2) When x < -1, replace |x+1| with -(x+1), because when x is less than -1, (x+1) will be negative and we negate it to make it positive (recall that the absolute value of a number is always positive). So, y = 14*(-x-1) + 2. Simplifying, we get y = -14x - 12, hence g(x) = -14x - 12 with a domain x < -1.
So to summarize, our absolute value function breaks into two linear functions as follows:
For x ≥ -1, f(x) = 14x + 16
And, for x < -1, g(x) = -14x - 12