# Let f, g and h be functions defined as follows:

• Jaco Viljoen
In summary, by defining functions f, g, and h, we can represent and analyze relationships between variables. These functions have different domains and ranges, allowing them to model different types of relationships. They can also be related through composition, creating more complex relationships and understanding the effects of changes in variables. However, functions have limitations in terms of their domains and ranges, and may not be suitable for all types of data or situations. In real-world applications, functions are widely used in science and engineering to model and analyze various phenomena and make informed decisions.
Jaco Viljoen

## Homework Statement

f(x)=(√x2-3x+2)/(2x-3), g(x)=3/(√x+3) and h(x)=(x2-5x+6)/(x-2)

which of the following are true:
A)Df={x∈ℝ:x≤1 or x≥2}
B)Dg={x∈ℝ:x≥-3}
C)Dh=ℝ

## The Attempt at a Solution

I am only attempting now,

Jaco Viljoen said:

## Homework Statement

f(x)=(√x2-3x+2)/(2x-3), g(x)=3/(√x+3) and h(x)=(x2-5x+6)/(x-2)

which of the following are true:
A)Df={x∈ℝ:x≤1 or x≥2}
B)Dg={x∈ℝ:x≥-3}
C)Dh=ℝ

## The Attempt at a Solution

I am only attempting now,
Let us know what your attempt is when you get it finished.

Jaco Viljoen

## 1. What is the purpose of defining functions f, g, and h?

Functions are mathematical tools that allow us to represent relationships between variables. By defining functions f, g, and h, we can analyze and understand how these variables relate to each other.

## 2. Can you explain the difference between f, g, and h?

Function f takes in a single input and produces a single output. Function g takes in two inputs and produces a single output. Function h takes in two inputs and produces two outputs. This means that f, g, and h have different domains and ranges and can be used to model different types of relationships.

## 3. How are functions f, g, and h related to each other?

Functions f, g, and h can be related through composition, which means that the output of one function can serve as the input for another function. This allows us to create more complex relationships and understand how changes in one variable affect the others.

## 4. Are there any limitations to using functions f, g, and h?

Functions have certain restrictions in terms of their domains and ranges. This means that not all values of the input variable can produce valid outputs. Additionally, functions can only represent certain types of relationships and may not be suitable for all types of data or situations.

## 5. How can functions f, g, and h be used in real-world applications?

Functions are widely used in various fields of science and engineering to model and analyze real-world phenomena. For example, they can be used to predict the trajectory of a projectile, describe the growth of a population, or analyze the behavior of a chemical reaction. By understanding the relationships between variables, we can make informed decisions and solve complex problems.

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