How do you find the inverse of a function? Here's some simple steps.
Suppose f(x) = 3x + 8
1. Substitute f(x) with y
2. Interchange y and x
3. Solve equation for y
In this example f(x) = 3x + 8 becomes y = 3x + 8.
Next interchange x and y to get x = 3y + 8.
Now solve equation for y to get (x - 8)/3 = y
If you have two functions and you want to determine if they are inverses of each other, find the inverse of each. If the inverse matches the opposite function, then the functions are inverses.
For example, f(x) = x^2 and g(x) = square root(x). Get the inverse of f(x) first, which is
y = x^2
x = y^2
Solve for y to get y = square root(x) which is g(x).
Now get the inverse of g(x)
y = square root(x)
x = square root(y)
solve for y to get y = x^2, which is f(x). Therefore, f(x) and g(x) are inverses.