Question

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

Answer 1

Answer:

The value of $f^{-1}(2)=8$

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

∵ $f(x)=log_{4}(x + 8)$

- Write the function as y = f(x)

∴ $y=log_{4}(x+8)$

- Switch x and y

∴ $x=log_{4}(y+8)$

- Lets solve it to find y

# Remember: $log_{a}b=n=====a^{n}=b$

- Use this rule to find y

∴ $4^{x}=(y + 8)$

- Subtract 8 from both sides

∴ $4^{x}-8=y$

∴ $f^{-1}(x)=4^{x}-8$

- Lets substitute x by 2

∴ $f^{-1}(2)=4^{2}-8$

- The value of 4² = 16

∴ $f^{-1}(x)=16-8=8$

* The value of $f^{-1}(2)=8$