Answer :
We need to find the inverse function of:
[tex]f\mleft(x\mright)=−3x+4[/tex]In order to do so, we can:
• replace x with y;
,• replace f(x) with x;
,• isolate y on the left side;
,• replace y with f⁻¹(x).
We obtain:
[tex]\begin{gathered} x=-3y+4 \\ \\ x+3y=-3y+4+3y \\ \\ 3y+x=4 \\ \\ 3y+x-x=4-x \\ \\ 3y=4-x \\ \\ \frac{3}{3}y=\frac{4-x}{3} \\ \\ y=-\frac{1}{3}x+\frac{4}{3} \\ \\ f^{-1}\left(x\right)=-\frac{1}{3}x+\frac{4}{3} \end{gathered}[/tex]Answer: option C
[tex]f^{-1}(x)=-\frac{1}{3}x+\frac{4}{3}[/tex]