Question 479561
Algebraically speaking, if f(x) = -x + b, then {{{f^(-1) = -x + b}}}, also, because {{{(f o f^(-1))(x) =  -(-x+b) + b = x - b + b = x}}}, which would satisfy the definition of an inverse function for f(x).
Graphically speaking, the graph of {{{f^(-1)}}} in general is just the symmetric rotation of the graph of f(x) about the line y = x. Since the line y = -x + b is perpendicular to the line y = x, a single symmetric rotation about the line y = x would yield the same graph, meaning the inverse function must be equal to itself.