Question

Question 71?Graph each function and it’s inverse on same set axes? Label two points on graph?

Answer 1

See graph below

Step-by-step explanation:
`\begin{gathered} 71)\text{ Given}\colon \\ y=log_6\text{ x} \end{gathered}`

To find the inverse of the function, 1st we'll interchange x and y:

`\begin{gathered} x=log_6y \\ \text{from log rules:} \\ if\text{ }a=\log _bC,\text{ then }b^a\text{ = C} \\ \\ \text{Applying that to the function we have: }x=log_6y \\ 6^x\text{ = y} \\ In\text{verse of the function = }f^(-1)(x) \\ f^(-1)(x)=6^x \end{gathered}`

plotting both graphs on the same axes:

`\begin{gathered} y\text{ = }log_6x\text{ and} \\ y=6^x\text{ (uinverse function)} \end{gathered}`

The points on both lines is at when x = 0 and x = 1

`\begin{gathered} \text{for }y\text{ = }log_6x\text{ } \\ \text{when x = 6, y = }1 \\ \text{when x = 1, y = }0 \\ \\ y=6^x\text{ (uinverse function)} \\ \text{when x = 0, y = }1 \\ \text{when x = 1, y = 6} \end{gathered}`