Inverse Of A Function

We have learnt that a function f maps x to f(x).
The inverse of f is a function which maps f(x) to x in reverse.
The inverse of the function f is denoted by f^-1.

The inverse of a function is found by interchanging its range and domain. The domain of F becomes the range of the inverse and the range of F becomes the domain of the inverse of F. The inverse of a function is not always a function and should be checked by the definition of a function.

Example:

If f(x) = x + 3 then f^-1(x) = x – 3

If g(x) = 4x then g^-1(x) =

You may wonder how we get the definitions of f^-1(x) and g^-1(x) in the above example.

The steps involved in getting the inverse of a function are:

Step 1:. Replace f(x) with y

Step 2: Move y to the right side of the equation

Step 3: Make x the subject of the equation

Srep 4: Replace x by f-1(x) and replace y by x

The following example illustrates these steps.

Example:

Find the inverse of each of the following functions:

a) f(x) = 2x + 3

b) g(x) = – 5

c) h(x) =

Solution:

a) Rewrite f(x) = 2x + 3 as y = 2x + 3.

Videos

Understanding inverse functions -
Professor Edward Burger explains inverse functions.

Finding the inverse of a function -
Professor Edward Burger explains how to find the inverse of a function

Are two functions inverses of each other -
Professor Edward Burger explains how to determine whether two functions are inverses of each other.

Finding the inverse of a function with higher powers -
Professor Edward Burger explains finding the inverse of a function with higher powers.

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