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Sagot :
Let's begin by listing out the information given to us:
[tex]\begin{gathered} f\mleft(x\mright)=\frac{1}{5}x+6 \\ f(x)=y \\ y=\frac{1}{5}x+6 \end{gathered}[/tex]To find the inverse, of this equation, we have to interchange the two variables (x for y). We have:
[tex]\begin{gathered} y=\frac{1}{5}x+6\Rightarrow x=\frac{1}{5}y+6 \\ x=\frac{1}{5}y+6 \\ \text{Multiply through each element by 5, we have:} \\ 5\cdot x=\frac{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}[/tex]
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