Returning a function from a function means that a function is created and returned as output of another function. This is possible in Python because functions are first-class objects, which means they can be passed around just like any other object such as integers, strings, or lists.

## Return function in Python

In next example, `function1`

returns a function `function2`

that multiplies its argument by `a`

. When `function1(5)`

is called, it returns `function2`

with `a`

set to `5`

. This returned function is stored in the variable `multiply_by_5`

. We can then call `multiply_by_5(3)`

to get the result of `15`

.

### Example 1: Simple use of function return

```
def function1(a):
def function2(b):
return a * b
return function2
multiply_by_5 = function1(5)
result = multiply_by_5(3)
print(result) # Output: 15
```

### Example 2: Add or multiply

```
def function3(operation):
def add_numbers(a, b):
return a + b
def multiply_numbers(a, b):
return a * b
if operation == "add":
return add_numbers
elif operation == "multiply":
return multiply_numbers
operation_type = "add"
math_function = function3(operation_type)
result = math_function(3, 5)
print(result) # Output: 8
```

In this example, `function3`

returns either the `add_numbers`

function or the `multiply_numbers`

function based on the value of the `operation`

parameter. If `operation`

is `"add"`

, the `add_numbers`

function is returned and if `operation`

is `"multiply"`

, the `multiply_numbers`

function is returned. The returned function is then stored in the `math_function`

variable. We can then call `math_function(3, 5)`

to add or multiply the two numbers based on the value of `operation_type`

. In this case, since `operation_type`

is `"add"`

, the output is `8`

which is the sum of `3`

and `5`

.

## Exploring the concept of nested functions and returning functions

In Python, functions can be nested, which means you can define one function inside another function. You can also return a function from another function. This concept of nested functions and returning functions allows for more flexibility and is a powerful tool in programming.

### Example 1: Returning a function from a function

```
def create_adder(num):
def adder(x):
return num + x
return adder
add5 = create_adder(5)
print(add5(3)) # Output: 8
```

In this example, we define a function `create_adder`

that takes a parameter `num`

. Inside `create_adder`

, we define another function `adder`

that takes a parameter `x`

and returns the sum of `num`

and `x`

. Finally, `create_adder`

returns `adder`

.

We then create a new function `add5`

by calling `create_adder(5)`

. This means that `add5`

is now a reference to `adder`

with `num`

set to 5. When we call `add5(3)`

, we pass the parameter `x`

as `3`

, which results in the output `8`

.

### Example 2: Nested functions

```
def outer_function(num):
def inner_function(x):
return num + x
return inner_function
add3 = outer_function(3)
add5 = outer_function(5)
print(add3(10)) # Output: 13
print(add5(10)) # Output: 15
```

In this example, we define a function `outer_function`

that takes a parameter `num`

. Inside `outer_function`

, we define another function `inner_function`

that takes a parameter `x`

and returns the sum of `num`

and `x`

. Finally, `outer_function`

returns `inner_function`

.

We then create two new functions `add3`

and `add5`

by calling `outer_function(3)`

and `outer_function(5)`

respectively. This means that `add3`

is now a reference to `inner_function`

with `num`

set to 3, and `add5`

is a reference to `inner_function`

with `num`

set to 5. When we call `add3(10)`

and `add5(10)`

, we pass the parameter `x`

as `10`

, which results in the output `13`

and `15`

respectively.

## Understanding the advantages of returning a function from another function

One of the significant benefits of returning a function from another function in Python is that it provides flexibility. By returning a function, the programmer can create a more specific and customized function based on the inputs passed to the original function. It also allows for efficient code reuse.

Another advantage of returning a function from another function is that it can simplify code complexity, leading to a more readable code structure. The code becomes more organized and understandable, thus enhancing its maintenance and debugging processes.

Here are two examples of returning a function from a function in Python:

### Example 1: Returning a function that multiplies any number by a given factor:

```
def multiply(factor):
def inner(num):
return num * factor
return inner
double = multiply(2)
triple = multiply(3)
print(double(5)) #output: 10
print(triple(5)) #output: 15
```

By calling `multiply(2)`

and `multiply(3)`

, we create two new functions `double`

and `triple`

, respectively, that can be used to multiply any number by `2`

or `3`

.

### Example 2: Returning a function that performs mathematical operations:

```
def operate(operation):
def inner(num1, num2):
if operation == 'add':
return num1 + num2
elif operation == 'subtract':
return num1 - num2
elif operation == 'multiply':
return num1 * num2
elif operation == 'divide':
return num1 / num2
return inner
add_func = operate('add')
subtract_func = operate('subtract')
print(add_func(10, 5)) #output: 15
print(subtract_func(10, 5)) #output: 5
```

By calling `operate('add')`

and `operate('subtract')`

, we create two new functions `add_func`

and `subtract_func`

, respectively, that can be used to perform addition and subtraction operations on any two numbers.

## Understanding the different ways of defining and returning functions in Python

Returning a function from a function can be useful in situations where we need to create functions dynamically based on certain conditions.

```
def create_adder(num):
def adder(x):
return x + num
return adder
add5 = create_adder(5)
print(add5(10)) # Output: 15
```

In this example, we define a function called `create_adder`

that takes a `num`

parameter. Within the `create_adder`

function, we define another function called `adder`

that takes an `x`

parameter and returns the sum of `num`

and `x`

. Finally, we return the `adder`

function as an output.

We then assign the output of `create_adder(5)`

to a variable called `add5`

. This means that `add5`

is now a function that takes a parameter `x`

and returns the sum of `5`

and `x`

. When we call `add5(10)`

, it returns `15`

.

## Exploring the use arguments in returned functions

```
def power(base):
def exponent(exp):
return base ** exp
return exponent
square = power(2)
cube = power(3)
print(square(5)) # Output: 25
print(cube(3)) # Output: 27
```

In this example, a nested function `exponent`

is defined inside the `power`

function. The `exponent`

function calculates a number raised to a power. The `power`

function returns the `exponent`

function. Two variables `square`

and `cube`

are assigned by calling the `power`

function with different base values. The final two print statements call `square`

and `cube`

with different exponent values.

```
def operation(operator):
def calculate(num1, num2):
if operator == '+':
return num1 + num2
elif operator == '-':
return num1 - num2
elif operator == '*':
return num1 * num2
elif operator == '/':
return num1 / num2
else:
return "Invalid operator"
return calculate
addition = operation('+')
subtraction = operation('-')
multiplication = operation('*')
division = operation('/')
print(addition(5, 3)) # Output: 8
print(subtraction(5, 3)) # Output: 2
print(multiplication(5, 3)) # Output: 15
print(division(5, 3)) # Output: 1.6666666666666667
print(operation('%')(5, 3)) # Output: Invalid operator
```

In this example, the `operation`

function takes an `operator`

parameter and returns the `calculate`

function. The `calculate`

function performs the arithmetic operation specified by the `operator`

parameter on two number arguments. Four variables `addition`

, `subtraction`

, `multiplication`

, and `division`

are assigned by calling the `operation`

function with different operator values. The final print statement shows what occurs when an invalid operator is used as an argument.