All categories

2 years ago

What is the domain of the function f(x) = 2x^2 - 3?

1 answer:

4 0

Domain: Set of all real numbers

If you want to express the domain in set-builder notation, then you'd write something like $\left\{x|x\in\mathbb{R}\right\}$ which is fancy notation to basically say "x is any real number"

If you want to write the domain in interval notation, then you'd write $\left(-\infty, \infty\right)$ which is the interval from negative infinity to positive infinity. In other words, the entire real number line.

-----------------------------------------------------------------

The domain is the set of all real numbers because we don't have any restrictions to worry about. There are no division by zero errors. There are no cases where we have to worry about taking the square root of a negative number, or anything similar. Any number can replace x to generate an output for y.

You might be interested in

a square has a side length of x. A rectangle has a length that is 4 inches longer than the square and a width that is 2 inches s

vodomira [7]

Answer:

Length of the rectangle is = 8 inches.

Step-by-step explanation:

Given :

Area of square = Area of the rectangle

According to the question:

Length of the square be 'x'.

Its area = (Side)*(Side) = $x^2$ ...equation (i)

Length of the rectangle = $(x+4)$

Width of the rectangle = $(x-2)$

Area of the rectangle =Length * Width

⇒ $(x+4)(x-2)=x^2-2x+4x-8$

⇒ $x^2+2x-8$ ...equation (ii)

Equating both the equation as area of both the figure are equal.

⇒ $x^2+2x-8=x^2$

⇒ $2x-8=0$ ...subtracting $x^2$ both sides

⇒ $2x=8$ ...dividing both sides with 2

⇒ $x=\frac{8}{2}=4$ inches

Plugging the value of x=4 in the length of the rectangle.

We have,

⇒ $(x+4)=(4+4)=8$

So the length of the rectangle = 8 inches.

4 0

3 years ago

Exercise 2.4.2: Proving statements about rational numbers with direct proofs. About Prove each of the following statements using

IgorLugansk [536]

Answer:

See Explanation

Step-by-step explanation:

(a) Proof: Product of two rational numbers

Using direct proofs.

Let the two rational numbers be A and B.

Such that:

$A = \frac{1}{2}$

$B = \frac{2}{3}$

The product:

$A * B = \frac{1}{2} * \frac{2}{3}$

$A * B = \frac{1}{1} * \frac{1}{3}$

$A * B = 1 * \frac{1}{3}$

$A * B = \frac{1}{3}$

Proved, because 1/3 is rational

(b) Proof: Quotient of a rational number and a non-zero rational number

Using direct proofs.

Let the two rational numbers be A and B.

Such that:

$A = \frac{1}{2}$

$B = \frac{2}{3}$

The quotient:

$A / B = \frac{1}{2} / \frac{2}{3}$

Express as product

$A / B = \frac{1}{2} / \frac{3}{2}$

$A / B = \frac{1*3}{2*2}$

$A / B = \frac{3}{4}$

Proved, because 3/4 is rational

(c) x + y is rational (missing from the question)

Using direct proofs.

Let x and y be

Such that:

$x = \frac{1}{2}$

$y = \frac{2}{3}$

The sum:

$x + y = \frac{1}{2} + \frac{2}{3}$

Take LCM

$x + y = \frac{3+4}{6}$

$x + y = \frac{7}{6}$

Proved, because 7/6 is rational

<em>The above proof works for all values of A, B, x and y; as long as they are rational values</em>

8 0

3 years ago

Is 1/2 greater than 4/5

Law Incorporation [45]

For this question you should know:
1/2 = 5/10
and
4/5 = 8/10
so you can see 8/10 is greater than 5/10 so the answer is no
4/5 is greater than 1/2 :)))
i hope this is helpful
have a nice day

4 0

3 years ago

How many sixteenths are there in 5/8

nadya68 [22]

Answer:

10!

Step-by-step explanation:

Exuse me if im wrong :')

6 0

3 years ago

14,219.92 The 9 in the ones place is _______ the value of the 9 in the tenths place.

Elza [17]

Answer:

less

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

What is the domain of the function ​f(x) = 2x^2 - 3​?

What is the domain of the function f(x) = 2x^2 - 3?