Step 1
Given;
Step 2
[tex]\begin{gathered} y=f(x) \\ Thus, \\ y=-19x+13 \\ \mathrm{A\:function\:g\:is\:the\:inverse\:of\:function\:f\:if\:for}\:y=f\left(x\right),\:\:x=g\left(y\right)\: \\ replace\text{ y with x and x with y} \\ x=-19y+13 \end{gathered}[/tex]
Solve for y
[tex]\begin{gathered} 19y=13-x \\ \frac{19y}{19}=\frac{13-x}{19} \\ y=\frac{13-x}{19} \\ f^{-1}(x)=\frac{13-x}{19} \end{gathered}[/tex]
Answer; Option C
[tex]f^{-1}(x)=\frac{13-x}{19}[/tex]
