Answer:
[tex]h^{-1}(x)=\dfrac{5x+4}{1-x}[/tex]
Step-by-step explanation:
Write the given expression in terms of y and x:
[tex]y=\dfrac{x-4}{x+5}[/tex]
Then swap the positions of x and y, and solve for y.
[tex]x=\dfrac{y-4}{y+5}\\\\xy+5x=y-4 \qquad\text{multiply by y+5}\\\\5x+4=y-xy \qquad\text{add 4-xy}\\\\\dfrac{5x+4}{1-x}=y \qquad\text{divide by the coefficient of y}\\\\h^{-1}(x)=\dfrac{5x+4}{1-x} \qquad\text{put in function form}[/tex]
