To solve for the inverse of the function given;
[tex]f(x)=x-9[/tex]
We begin by re-writing the function as follows;
[tex]y=x-9[/tex]
To now find the inverse, we interchange y for x, and vice versa, as shown below;
[tex]\begin{gathered} y=x-9 \\ \text{Now becomes;} \\ x=y-9 \end{gathered}[/tex]
We now find the value of y;
[tex]\begin{gathered} x=y-9 \\ \text{Add 9 to both sides;} \\ x+9=y-9+9 \\ x+9=y \\ y=x+9 \\ \text{Therefore;} \\ f^{-1}(x)=x+9 \end{gathered}[/tex]
ANSWER:
The correct answer is option B;
[tex]f^{-1}(x)=x+9[/tex]
