Determine the domain and range for the inverse of f(x)=1/4x+2

Answer 1

To determine the domain and range of the inverse of f(x) = 1/4x + 2, we first need to find the inverse function:

Let y = f(x)
1/4x + 2 = y
1/4x = y - 2
x = 4(y - 2)
x = 4y - 8

Now we switch x and y:
y = 4x - 8

The domain of the inverse function is the range of the original function, and the range of the inverse function is the domain of the original function.

For the original function f(x) = 1/4x + 2, the domain includes all real numbers except x = 0 (since we can't divide by zero). So the domain is (-∞, 0) U (0, ∞).

The range of the original function f(x) = 1/4x + 2 is all real numbers. Therefore, the range of the inverse function y = 4x - 8 is also all real numbers.