Question

F(x) = 7x-2 what is the inverse

Answer 1

Let's begin by listing out the information given to us:

`\begin{gathered} f\mleft(x\mright)=7x-2 \\ f(x)=y \\ y=7x-2 \end{gathered}`

To calculate the inverse for this function, we interchange the variables x & y:

`\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:} \\ (1)/(7)x+(2)/(7)=(7y)/(7)\Rightarrow(1)/(7)x+(2)/(7)=y \\ y=(1)/(7)x+(2)/(7) \\ y=f(x) \\ f(x)=(1)/(7)x+(2)/(7) \\ \Rightarrow f(^(-1))=(1)/(7)x+(2)/(7) \end{gathered}`