How do you find the inverse of a function f(x), `f^-1(x)`?

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justaguide | College Teacher | (Level 2) Distinguished Educator

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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).

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