# Domain and Range of f(x,y)=2x^2+3x^2+1: Real Numbers and Minimum Value of 1

• seto6
In summary, the domain for the function f(x,y)=2x^2+3y^2+1 is all real numbers for both x and y, or \mathtype{R}^2. The range of the function is any number greater than or equal to 1, as the function can never produce a value less than 1.
seto6

## Homework Statement

Find the domain and the range

f(x,y)=2x2+3x2+1

non

## The Attempt at a Solution

...
i said that x,y are all real #'s

and f(x,y)>=1 or z>=1

is there anything wrong with what i has attempted at?

if do could you explain...

Last edited:
check out (x,y) = (-1,1).

what do you mean by that?

I assume you mean $f(x,y)=2x^2+3y^2+1$

First, the "natural" domain for a given formula is the set of all x values for which the formula can be calculated. There is no reason why we cannot square any number or multiply or add any numbers. The domain for this function, like the domain for any polynomial is "all real numbers" for both x and y or, more formally, $\mathtype{R}^2$.

A far as the range is concerned, we know that a square is never negative so neither $2x^2$ nor $3y^2$ can be less than 0. That means that $f(x,y)= 2x^2+ 3y^2+ 1$ is never less than 1 but can, of course, have any value above that.

(I have no idea what fluxions meant.)

The OP edited the function after my post. It was originally f(x,y) = 2x^2 + 3x^y + 1, and s/he made the claim that f(x,y) > 1 for all x,y. I suggested that was false, a counterexample being f(-1,1). Sorry for the confusion.

## What is a domain and range?

A domain is the set of all possible input values for a function, while the range is the set of all possible output values.

## How do you find the domain and range of a function?

To find the domain, look at the input values of the function and determine what values are allowed. To find the range, look at the output values and determine what values are produced.

## What does a domain and range look like on a graph?

On a graph, the domain is represented by the x-axis, and the range is represented by the y-axis. The domain is the horizontal axis and the range is the vertical axis.

## Can a function have multiple domains and ranges?

No, a function can only have one domain and one range. However, a function can have multiple inputs that produce the same output, so it may appear to have multiple ranges.

## How does the domain and range affect the behavior of a function?

The domain and range can affect the behavior of a function by limiting the possible input and output values. It can also determine if a function is continuous or discontinuous.

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