Question

What is the inverseof f(x)=x/5+6

Answer 1

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

`\begin{gathered} f\mleft(x\mright)=(1)/(5)x+6​ \\ f(x)=y \\ y=(1)/(5)x+6 \end{gathered}`

To find the inverse, of this equation, we have to interchange the two variables (x for y). We have:

`\begin{gathered} y=(1)/(5)x+6\Rightarrow x=(1)/(5)y+6 \\ x=(1)/(5)y+6 \\ \text{Multiply through each element by 5, we have:} \\ 5\cdot x=(1)/(5)y\cdot5+6\cdot5 \\ 5x=y+30 \\ \text{Subtract 30 from both side, we have:} \\ 5x-30=y+30-30 \\ 5x-30=y\Rightarrow y=5x-30 \\ y=5x-30 \\ f(^(-1))=5x-30 \end{gathered}`