Question

let f and g be thwe function from the set of integers to itself defined by f(X) =2x +1 and g (X)=3x+4 then the composition of f and g is​

Answer 1

Answer:

6x+9

Step-by-step explanation:

The composition of f and

g is given by f(g(x)) which is equal to

2(3x + 4) + 1.

Answer 2

Answer:

Step-by-step explanation:

Concept:

Sets:

In mathematics, a set is a logically arranged group of items that can be represented in either set-builder or roster form. Sets are typically denoted by curly brackets; for instance, A = {1, 2, 3, 4} is a set. Check the set symbols here as well.

The way that sets are represented by a person is always the same: as a group of clearly defined objects or elements. A capital letter designates a set. The cardinal number of a set is the number of elements in the finite set.

Function:

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as $f(x)$, where$x$ is the input.

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

Although some authors make a distinction between "maps" and "functions" (see Other terminology), functions are also referred to as maps or mappings.

If the domain and codomain sets of two functions f and g are the same and their output values match across the entire domain, then the two functions are equivalent. Formally, we have$f = g$if and only if $f(x) = g(x)$.

Given:

let$f$ and$g$ be the function from the set of integers to itself defined by $f(x)=2x+1$ and $g(x)=3x+4.$

Find:

the composition of$f$and $g$.

Solution:

given that let$f$and $g$ be the function from the set of integers to itself defined by

$f(x)=2x+1$

$g(x)=3x+4$

$f(g(x))=2(3x+4)+1$

$f(g(x))=6x+8+1$

$f(g(x))=6x+9$

Hence  the composition of f and g is given by f(g(x)) which is equal to 6x+9.

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