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3 years ago

Determine the range of the inverse of f(x) = 2x + 1

Mathematics

2 answers:

aleksandrvk [35]3 years ago

7 0

Answer:

The range is all real numbers for the inverse

Step-by-step explanation:

f(x) = 2x+1

The domain is all real numbers

The range is all real numbers

For the inverse, the domain becomes the range

The range becomes the domain

The domain is all real numbers

The range is all real numbers

Bingel [31]3 years ago

7 0

Step-by-step explanation:

Given the function f(x) = 2x + 1

find : the range of the inverse of f(x) = 2x + 1

solutions:

f(x) = 2x + 1

y = 2x + 1

2x = y - 1

x = (y -1)/2

f~¹(x) = (x-1) /2

since the denominator is the constant number, so the range of function is all Real numbers

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The volume is 27 cubic cm.

Step-by-step explanation:

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4 years ago

The Jaxon High School prom committee has 100 thumb drives to sell in a fundraiser. The function f(x) = 8x – 200 models their inc

Alina [70]

Answer:

25 = x

Step-by-step explanation:

Based on the equation we see that the thumb drives cost $200 which is why that is being subtracted. To calculate the break-even number of sales we need to make a total of 200 to cover the costs. We calculate this by matching the equation to 0 and solving for x...

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2 years ago

Order the following numbers from least to greatest.

zaharov [31]

Answer:

-5.5 $-\sqrt{20}$ $\sqrt4$ $\frac{22}{7}$ 4.5

Step-by-step explanation:

Given:

The numbers to order from least to greatest is given as:

$-5.5, 4.5, 22/7,\sqrt4,-\sqrt{20}$

In order to compare these numbers, we have to convert them in same form.

Let us simplify each number in decimal form.

$-5.5 = -5.5\\\\4.5=4.5\\\\\frac{22}{7}=3.14\\\\\sqrt4=2\\\\-\sqrt{20}=-\sqrt{5\times 2^2}=-2\sqrt5=-4.47$

So, the least number is one which has the largest value with a negative sign.

Here, -5.5 is the least number.

The next smallest number is -4.47. So, $-\sqrt{20}$

The next smallest number is 2. So, $\sqrt4$

The next smallest number is 3.14. So, $\frac{22}{7}$

The greatest number is 4.5.

Therefore, the order from the least to greatest is:

-5.5 < $-\sqrt{20}$ < $\sqrt4$ < $\frac{22}{7}$ < 4.5

8 0

3 years ago

PLSSS HELP IF YOU TURLY KNOW THISS

grigory [225]

<h2>Answer:</h2>

The answer is x = 2.

<h2>Step-by-step explanation:</h2>

* Scroll to the bottom for an explanation in list format :)

In this problem, our goal is to solve for x in order to identify said variable's value. To do this, we must isolate the variable x on one side, whilst the other side contains solely the value of x. The rules that we will be using for this problem are 'Line of Equality' and 'PEMDAS.' Line of Equality is a rule that states that what you do to one side of an inequality/equation, you must to do the other as well. PEMDAS is a mathematical acronym used as a tell-tale of sorts for order of operations - often OoO for inequalities such as this one. In PEMDAS, P stands for Parenthesis, E stands for Exponents, M stands for Multiplication, D stands for Division, A stands for Addition, and S stands for Subtraction. You use each letter in order of the spelling, with the exception that you do Multiplication and Division by whichever comes first in the equation; the same goes for Addition and Subtraction. However, when solving this inequality, we won't have to focus on the complications of P, E, or M at all.

The (original) inequality this problem gives us is 14 + 3x = 2 + 9x. Our first step is to choose which side we will isolate x to, leaving the other one to be its value. I would personally recommend isolate whichever x value is greater, but either way works. This time around, I chose to isolate 9x.

Since I've decided to isolate x on the right side (2 + 9x), that means I have to eliminate any other x values on either side of the inequality. The only other x value is 3x. Due to + 3x being adding a positive 3x, we have to counteract it by eliminating it and changing its value to 0. In this case, we can counteract + 3x by subtracting 3x (aka - 3x). Remember, the Line of Equality rule means we have to do the same to either side; if we subtract 3x on one side, we also have to do so on the other. 14 + 3x - 3x = 2 + 9x - 3x. +3x - 3x = 0, or 0x. 9x - 3x = 6x. After combining like terms, the new inequality is 14 = 2 + 6x.

Now, I have to eliminate any numerical values, or regular numbers (which, in this case, would be numbers without a variable attached to them), on the right side, since that is the side I want to isolate x on. The only numerical value on the right side of my inequality is 2. This 2, or + 2, can be counteracted by subtracting 2, or - 2. Our rule causes us to subtract 2 from both sides. 14 - 2 = 2 - 2 + 6x. 14 - 2 = 12. 2 - 2 = 0. After combining like terms, the new inequality is 12 = 6x.

Now, I have to simplify x and make it singular. 1x and x are the same thing, so I must make 6x into x. 6x is the same thing as 6 * x. Therefore, since 6 * x is multiplication, I have to do the opposite to get the desired result. I should divide 6x by 6 to get 6. Due to the Line of Equality, I also have to divide 12 by 6. 12 ÷ 6 = 6x ÷ 6. 12 ÷ 6 = 2. 6x ÷ 6 = x. After combining like terms, the new inequality is 2 = x.

Lastly, mainly for a bonus step, we should flip the places of 2 and x. This is because, similarly to most problems, this question places x on the left side of the inequality. The 2 and x in 2 = x must switch places in order to properly finish this problem. Since this inequality uses an equal sign, the symbol will remain as an = when the inequality is flipped. However, it should be noted that when using symbols such as greater than (>) or less than (<), the sign will flip with the rest of the inequality. = is a symmetrical sign, which is why it will remain the same; it is the same equivalent symbol even when flipped. After we flip the inequality, the new equation becomes x = 2. Therefore, our answer is x = 2.

<h3>For those that want a list format of the procedure for this inequality's solving - here you go: </h3>

* Remember the 'Line of Equality' Rule: What you do on one side, on the other do the same.

14 + 3x = 2 + 9x

Subtract 3x from both sides.

14 + 3x - 3x = 2 + 9x - 3x

14 = 2 + 6x

Subtract 2 from both sides.

14 - 2 = (+)2 - 2 + 6x

12 = 6x

Divide both sides by 6.

12 ÷ 6 = 6x ÷ 6

2 = x

Flip the inequality. (The sign remains the same since it's the equal sign.)

x = 2

Therefore, our answer is x = 2.

7 0

3 years ago

What is the value of x in the equation 8x – 2y = 48, when y = 4? 6 7 14 48

natita [175]

Answer:

x=7

Step-by-step explanation:

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3 years ago