[tex]h(x)=-2x+5\to y=-2x+5\\\\\text{Interchange the y and the x}\\\\x=-2y+5\\\\\text{Solve for y}\\\\-2y+5=x\qquad|-5\\\\-2y=x-5\qquad|:(-2)\\\\y=\dfrac{x-5}{-2}\\\\y=-\dfrac{1}{2}x+\dfrac{5}{2}\\\\Answer:\ \boxed{h^{-1}(x)=-\dfrac{1}{2}x+\dfrac{5}{2}}[/tex]
