MATHEMATICS MIDDLE SCHOOL

Let f(x)=2/x-3. Find f^-1(x)

Answers

Answer 1

Answer:

Answer:

Two questions:

Question 1: $f^(-1)(x)=?$ given $f(x)=(2)/(x)-3$ .

Answer 1: $f^(-1)(x)=(2)/(x+3)$

Question 2: $f^(-1)(x)=?$ given $f(x)=(2)/(x-3)$ .

Answer 2: $f^(-1)(x)=(2)/(x)+3$

Step-by-step explanation:

So $f^(-1)$ is used in most classes to represent the inverse function of $f$ .

The inverse when graphed is a reflection through the y=x line. The ordered pairs $(a,b)$ on $f$ implies $(b,a)$ are on $f^(-1)$ .

This means we really just need to swap x and y.

Since we want to write as a function of x we will need to solve for y again.

Question 1:

$y=(2)/(x)-3$

Swap x and y:

$x=(2)/(y)-3$

We want to solve for y.

Add 3 on both sides:

$x+3=(2)/(y)$

Make the left hand side a fraction so we can cross-multiply:

$(x+3)/(1)=(2)/(y)$

Cross multiply:

$y(x+3)=1(2)$

Simplify right hand side:

$y(x+3)=2$

Divide both sides by (x+3):

$y=(2)/(x+3)$

So $f^(-1)(x)=(2)/(x+3)$ .

Question 2:

$y=(2)/(x-3)$

Swap x and y:

$x=(2)/(y-3)$

Make left hand side a fraction so we can cross multiply:

$(x)/(1)=(2)/(y-3)$

Cross multiply:

$(y-3)x=1(2)$

We have to distribute here:

$yx-3x=2$

Add 3x on both sides:

$yx=2+3x$

Divide boht sides by x:

$y=(2+3x)/(x)$

You could probably stop here but you could also simplify a little.

Separate the fraction into two terms since you have 2 terms on top bottom being dividing by x:

$y=(2)/(x)+(3x)/(x)$

Simplify second fraction x/x=1:

$y=(2)/(x)+3$

So $f^(-1)(x)=(2)/(x)+3$ .

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the recipe for pumpkin dog biscuits is 2 eggs 1/2 cup canned pumpkin 1/2 teaspoon salt 2 tablespoons dry milk and! 2 1/2 cups wheat flour this recipe makes about 20 treats rewrite the recipe for 10 biscuits

Answers

1 egg
.25 cup canned pumpkin
.25 teaspoon salt
1 tablespoon dry milk
1.25 cups wheat flour

Wouldnt yuu just cut all the ingredients in half

which figure appears to have only 1 line of symmetry AND YOU ARE GOING TO HAVE TO OPEN THE PICTURE FOR YOU TO SEE THE QUESTION

Answers

The answer is A. Because you can only fold it up and down and it matches the other side of the folded crease. You can't any other way.
Plus, if you folded B it would be the same, but you can fold it more than once, and if you try to fold C. and D. they wouldn't match the other side of the folded crease.

Hope I Helped!!!

the answer is .......A

X + 3y = 5
-x + 6y = 4

Answers

Answer:

x=2, y=1. (2, 1).

Step-by-step explanation:

x+3y=5

-x+6y=4

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9y=9

y=9/9

y=1

x+3(1)=5

x+3=5

x=5-3

x=2

Copy each statement. Insert +,-,x, or ÷ symbols to make this statement true. 33-3-2-5=1

Answers

$\boxed{33 / 3-2 * 5=1} \n11-10=1 \n1=1$

Final answer:

To make the equation 33-3-2-5 equal to 1, the necessary mathematical operations are subtraction, multiplication, and addition. So, by replacing some of the minus signs in the equation, the true equation is: 33 - 3 x 2 + 5 = 1.

Explanation:

The task here is to find and replace the minus (-) signs with other mathematical operations (+, -, x, ÷) to make the equation true. We need to turn 33-3-2-5 into 1. After replacing the signs, the correct equation would be: 33 - 3 x 2 + 5 = 1.

Step-by-Step Explanation:

Consider the given problem: 33 - 3 - 2 - 5
We are asked to replace the signs to make it equal to 1.
Replace the first '-' sign to '-', the second '-' sign to 'x', and the third '-' sign to '+' sign.
The new equation is: 33 - 3 x 2 + 5.
As per the BIDMAS/BODMAS rule, which stands for Brackets, Indices, Division and Multiplication, Addition and Subtraction, multiplication comes before addition and subtraction.
First, do the multiplication: 3 x 2 = 6.
Now, simplify the equation: 33 - 6 + 5 = 32.
The statement now sums up to 1, making it a true statement.

Learn more about Order of Operations here:

brainly.com/question/15840745

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Given that a = 4, b = 3, c = 2, and d = 1, which gives the correct order from least to greatest for the rational numbers on a number line?

Answers

Least to greatest would mean going from the smallest number to the biggest. So it would be d,c,b,a

Final answer:

The correct order from least to greatest for the rational numbers given is d < c < b < a.

Explanation:

To find the correct order from least to greatest for the rational numbers, we need to compare the values of a, b, c, and d.

a = 4 is the greatest rational number.
b = 3 is the second greatest rational number.
c = 2 is the third greatest rational number.
d = 1 is the least rational number.

Therefore, the correct order from least to greatest is d < c < b < a.

Learn more about Ordering Rational Numbers here:

brainly.com/question/28337922

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What is 450 increased by 18%

Answers

450*(1+0.18)=531 hence 450 increased by 18% is 531

100% + 18% = 118%

118% as decimal = 1.18

450 times 1.18 = 531

answer: 531

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