Step-by-step explanation:
inverse means that x becomes y and y becomes x.
the domain (x) of f(x) is -6 <= x <= 4
the range (y) of f(x) is 1 <= y <= 4
for the inverse now
the domain is 1 <= x <= 4
the range is -6 <= y <= 4
so you start the graph at x = 1 and y = -6.
that connects with x = 2 and y = 1.
and that connects straight vertically up with x = 2 and y = 4.
that connects with x= 3 and y = 0.
and that connects with x = 4 and y = -1.
and that connects straight vertically down with x = 4 and y = -4.
when you look at the graph this is just reversing x and y. what was input before (x) is now result (y), and what was result before is now input.
it also tells us that the inverse is not a function, because here a single x value has in some cases (x = 2 and x = 4) multiple different y values associated (y = 1..4 and y = -1..-4).
