How do you find the inverse of a function f(x), `f^-1(x)`?
The inverse `f^-1(x)` of a function f(x) can be found in the following way.
Usually the graph of a function f(x) is written as y = f(x). All points on the graph represent (x, f(x)).
Take y = f(x) and rewrite it in a form where y is the independent variable and x is the dependent variable. It is possible to find the inverse of a function only where one value of f(x) does not correspond to more than one value of x.
For example, consider the function f(x) = 3x + 5
y = 3x + 5
Now express x as an expression with y
=> 3x = y - 5
=> x = (y - 5)/3
Therefore the inverse of f(x) is `f^-1(x) = (x - 5)/3`
In a similar manner the inverse of any function can be found if there is a one-to-one correspondence between x and f(x).