Question

Logs & Exponentials inding the inverse of f(x)=log((1/2)x+4) problem

Answer 1

To find the inverse of the given function, follow these steps: replace f(x) with y, swap x and y, solve for y, subtract 4 from both sides, and multiply both sides by 2.

Step-by-step explanation:

To find the inverse of the function f(x) = log((1/2)x + 4), we need to follow these steps:

1. Replace f(x) with y: y = log((1/2)x + 4)
2. Swap x and y: x = log((1/2)y + 4)
3. Solve for y: (1/2)y + 4 = 10^x
4. Subtract 4 from both sides: (1/2)y = 10^x - 4
5. Multiply both sides by 2: y = 2(10^x - 4)

So, the inverse of f(x) is f^(-1)(x) = 2(10^x - 4).