Answer:
D. [tex]f^{-1}(x)=-\frac{x}{2}+\frac{5}{2}[/tex]
Step-by-step explanation:
The given function is
[tex]f(x)=-2x+5[/tex]
Let
[tex]y=-2x+5[/tex]
Interchange x and y.
[tex]x=-2y+5[/tex]
Solve for y.
[tex]x-5=-2y[/tex]
[tex]\frac{x-5}{-2}=y[/tex]
[tex]\frac{x}{-2}-\frac{5}{-2}=y[/tex]
[tex]-\frac{x}{2}+\frac{5}{2}=y[/tex]
Therefore
[tex]f^{-1}(x)=-\frac{x}{2}+\frac{5}{2}[/tex]
