The first function is an inverse of the second and vice versa. Simply replace the 's in your function with 's to receive the inverse function.
Final Inverse of :
recall that for absolute values you have to consider two cases, when what's inside absolute value signs is negative and when it is positive.
to find the inverse, we switch x and y and solve for y:
work on each piece separately.
For the first graph:
for
For inverse, switch x and y:
for
for (which is equivalent to )
now for the second graph:
for
For inverse, switch x and y:
for
for (which is equivalent to )
thus, putting these together we have:
the graph is below. the green is , the red is