The inverse function of f(x) is denoted as f-1(x) and it represents the operation that undoes the original function. In this case, f-1(x) is the inverse of f(x) = -2x⁄3x - 4.
To find the explicit expression for f-1(x), we follow these steps:
1. Replace f(x) with y.
2. Solve the equation for x in terms of y.
3. Interchange x and y.
4. Replace y with f-1(x).
The domain of f-1(x) is the range of f(x), and the range of f-1(x) is the domain of f(x). In this case, the domain of f-1(x) is all real numbers except 4/3, and the range is all real numbers.
To verify if f-1(x) is the actual inverse of f(x), we can use the composition of functions method. We substitute f(x) into f-1(x) and simplify the expression. If the result is x, then f-1(x) is the inverse of f(x).
Yes, f-1(x) can be graphed on the same coordinate plane as f(x). The graph of f-1(x) is the reflection of the graph of f(x) over the line y = x. This means that the points (x, y) on the graph of f(x) will become (y, x) on the graph of f-1(x).