Question

Which of the following is the inverse of f(x) = - 19x + 13?OA.− 19 (x − 13)f¹(x) =OB. f¹(x) = 19 (x − 13)-OC. f-¹(x) = 130219OD. f¹(x) = x+1319

Answer 1

Step 1

Given;

Step 2

$\begin{gathered} y=f(x) \\ Thus, \\ y=-19x+13 \\ \mathrm{A\:function\:g\:is\:the\:inverse\:of\:function\:f\:if\:for}\:y=f\left(x\right),\:\:x=g\left(y\right)\: \\ replace\text{ y with x and x with y} \\ x=-19y+13 \end{gathered}$

Solve for y

$\begin{gathered} 19y=13-x \\ \frac{19y}{19}=\frac{13-x}{19} \\ y=\frac{13-x}{19} \\ f^{-1}(x)=\frac{13-x}{19} \end{gathered}$

Answer; Option C

$f^{-1}(x)=\frac{13-x}{19}$