Let's begin by listing out the information given to us:
[tex]\begin{gathered} f\mleft(x\mright)=7x-2 \\ f(x)=y \\ y=7x-2 \end{gathered}[/tex]To calculate the inverse for this function, we interchange the variables x & y:
[tex]\begin{gathered} y=7x-2\Rightarrow x=7y-2 \\ x=7y-2 \\ We\text{ want to make y the subject of formula} \\ \text{Add 2 to both side, we have:} \\ x+2=7y-2+2 \\ x+2=7y \\ \text{Divide through each element by 7, we have:} \\ \frac{1}{7}x+\frac{2}{7}=\frac{7y}{7}\Rightarrow\frac{1}{7}x+\frac{2}{7}=y \\ y=\frac{1}{7}x+\frac{2}{7} \\ y=f(x) \\ f(x)=\frac{1}{7}x+\frac{2}{7} \\ \Rightarrow f(^{-1})=\frac{1}{7}x+\frac{2}{7} \end{gathered}[/tex]