Inverse of a function is something that inverses the given function to get y = f-1(x). The inverse of inverse function is the function itself. For a given function y = f(x) is such that f-1(f(x)) = x for all the values of x for function f defined.

Inverse function Calculator find the inverse of any given function with respect to the variable, if the function is entered in the block provided.

## Inverse Function Problems

Here are some steps to solve the inverse function
Step 1 : Read the problem and note the given function y = f(x)
Step 2 : Solve the function x in terms of variable y.
Step 3 : Interchange the values x and y to get inverse function y = f-1(x).

Below are given some solved problems on inverse function which may be useful for you.

### Solved Examples

Question 1: Find the inverse function for the function f(x) = $\frac{x + 5}{x + 2}$
Solution:

Step 1: The Given function is y = $\frac{x + 5}{x + 2}$

Step 2: Solving for x
y(x + 2) = (x + 5)
xy + 2y = x + 5
xy - x = 5 - 2y
x = $\frac{5 - 2y}{y - 1}$

Step 3: Interchanging the values of x and y, we get
y = $\frac{5 - 2x}{x - 1}$.

Question 2: Find the inverse function for the function f(x) = 5x + 1.
Solution:

Step 1: The Given function is y = 5x + 1

Step 2:
Solving for x we get
5x = y - 1
x = $\frac{y - 1}{5}$

Step 3:
Interchanging the values of x and y, we get the inverse function
y = $\frac{x - 1}{5}$.

### Composite Function Calculator

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