how to verify if a function is inverse?

Answer 1

Inverse Functions
- A function g is the inverse of the function f if f(g(x)) for each x in the domain of g , and g(f(x)) for each x in the domain of f. The function g is denoted f^{-1}
- If g is the inverse of f , then f is the inverse of g
- The domain of f^{-1} is equal to the range of f, and the range of f^{-1} is equal to the domain of f
- The graph of f contains the point (a.b) if and only if the graph of f^{-1} contains the point (b,a) . Inverse functions are symmetric about the line y = x.
- A function possesses an inverse if and only if it is one-to-one.
Finding the Inverse of a Function:
- Determine whether the function y = f(x) has an inverse. It has an inverse if and only if it is one-to-one.
- Solve for x as a function of y
- Interchange x and y. The result is y = f^{-1}(x)
- Define the domain of f^{-1} to be the range of f
- Verify that f(f^{-1}(x)) = x and f^{-1}(f(x)) = x

Answer 2

First solve for X then Y. If both answers are real, it is inverse. For example:
2Y = 4X + 2
Y = 2X +1

4X = 2Y-2
X = 1/2Y - 1/2

Answer 3

If your function is f(x), just replace all x's with f(x) and f(x) with x and solve for f(x) to find its inverse.

Answer 4

try using the hroizantal line test on it instead of the vertical line test.