option D is correct.
Explanation:
[tex]\rightarrow \sf f(x) = 2x-9[/tex]
To find inverse, make x the subject
[tex]\rightarrow \sf f(x)+9 = 2x[/tex]
[tex]\rightarrow \sf x = \dfrac{ f(x)+9}{2}[/tex]
So the inverse is:
[tex]\rightarrow \sf g(x) = \dfrac{ x+9}{2}[/tex]
Rest all options are incorrect and is not inverse of each other.
