## Introduction

In mathematics, the function composition is an operation that takes two functions f and g and produces a new function h such that h(x) = g(f(x)). In other words, the function h is obtained by composing the functions f and g. The composition of functions is a very important concept in mathematics with many applications in different fields.

## What is the domain and range of a function?

The domain of a function is the set of all input values for which the function produces a result. The range of a function is the set of all output values for which the function produces a result.

## What is a function?

A function is a mathematical relation between two sets, usually denoted by an equation. The function assigns a unique output to every input. For example, the equation y = 3x + 2 defines a function because for every value of x there is a corresponding value of y. The input values are the numbers on the x-axis and the output values are the numbers on the y-axis.

## How to find the domain and range of a function?

To find the domain of a function, we need to find all the values of x for which the function produces a valid output. In other words, we need to find all the values of x for which the function produces a real output.

There are two cases to consider when finding the domain of a function:

-If the function is defined by an algebraic expression, then we can use algebra to find the domain.

-If the function is defined by a graph, then we can use our knowledge of graphing to find the domain.

The range of a function is the set of all output values that the function produces. In other words, it is the set of all y-values that we get when we input different x-values into our function. Just as with finding the domain, there are two cases to consider when finding the range of a function:

-If the function is defined by an algebraic expression, then we can use algebra to find the range.

-If the function is defined by a graph, then we can use our knowledge of graphing to find

## How to graph a function?

To graph a function, you need to find the points where the function intersects the x- and y-axes, and then plot those points. You can do this by using a graphing calculator, or by using a graph paper and a pencil.

## How to find the inverse of a function?

In mathematics, the inverse of a function is a function that “undoes” the original function. For example, the inverse of the function f(x) = 2x + 1 is the function g(x) = (x – 1)/2, which “undoes” the addition of 1, and then multiplies the result by 2.

In order to find the inverse of a function, you need to be able to solve equations. In particular, you need to be able to solve equations for variables that appear in both the original equation and the inverse equation. For example, in order to find the inverse of f(x) = 2x + 1, you need to be able to solve equations like 2g(x) + 1 = x for g(x).

Once you can do that, finding the inverse of a function is just a matter of reversing the roles of x and y in the original equation. So, for example, if f(x) = 2x + 1, then we can write down its inverse by interchanging x and y: g(y) = (y – 1)/2.

Of course, not all functions have inverses. In particular, many functions are not one-to-one functions, which means that some values of x correspond to more than one value of y. For example, the function f(x) = x^2 is not invertible because some values of x (such as 0) correspond to more than one value of y (in this case, both 0 and -0). In order for a function to have an inverse, it must be a one-to-one function.

## Conclusion

In conclusion, to find fxgx you need to multiply the two functions together. In this case, that would be 3×2 and 6×7. The answer would be fxgx= 42.