Given the function f(x) = log base 4(x+8) , find the value of f^-1(2)

The value of

Step-by-step explanation:

* Lets revise how to find the inverse function

- At first write the function as y = f(x)

- Then switch x and y

- Then solve for y

- The domain of f(x) will be the range of f^-1(x)

- The range of f(x) will be the domain of f^-1(x)

* Now lets solve the problem

- The inverse of the logarithmic function is an exponential function

∵

- Write the function as y = f(x)

∴

- Switch x and y

∴

- Lets solve it to find y

# Remember:

- Use this rule to find y

∴

- Subtract 8 from both sides

∴

∴

- Lets substitute x by 2

∴

- The value of 4² = 16

∴

* The value of

you need to show the graph

step-by-step explanation: