If point (a,b) lies on the graph y=f(x), the graph of f^-1 (x) must contain point:

Answers

Answer 1

Answer:

By the definition of inverse function,the point (a,b) lies on the graph $\bold{y= f(x).}$ So, (b,a) must be lies on the graph of $\bold{y=f^(-1) (x)}$ .

Given:

Point (a,b) lies on the graph y= f(x).

Find:

The graph of $\bold{y=f^(-1) (x)}$ must contain that point.

As per the definition of inverse function, if two one-to-one functions f(x) and g(x). If (f∘g)(x)=x and (g∘f)(x)=x. Then, we say that f(x) and g(x) are inverses of each other.

$\bold{f=\{ (x,y):x\epsilon R,y\epsilon R\}}$

Then, its inverse is defined as

$\bold{f^(-1) =\{ (y,x):x\epsilon R,y\epsilon R\}}$

Therefore, we have to interchange x and y-coordinate of the points which lies on the function f to get f⁻¹.

Thus, the point (a,b) lies on the graph $y= f(x).$ So, (b,a) must be lies on the graph of $y=f^(-1) (x)$ .

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Answer 2

Answer:

Given:

Point (a,b) lies on the graph $y=f(x)$ .

To find:

The point which is must be lies on the graph of $y=f^(-1)(x)$ .

Solution:

According to the definition of an inverse function, if a function is defined as

$f=\{(x,y):x\in R,y\in R\}$

then, its inverse is defined as

$f^(-1)=\{(y,x):x\in R,y\in R\}$

It means, we have to interchange x and y-coordinate of the points which lies on the function f to get f⁻¹.

We have a point (a,b) lies on the graph $y=f(x)$ . So, (b,a) must be lies on the graph of $y=f^(-1)(x)$ .

Therefore, the correct option is (1).

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the Alvarez family bought a car for $2,000 they made a down payment of $500 if they want to pay the balance in 5 equal payments how much would each of these payments be

Answers

Actual cost of the car bought by Alvarez family = $2000
Amount of down payment made by the Alvarez family = $500
Outstanding amount
that has to be paid by the Alvarez family = (2000 - 500) dollars
= 1500 dollars
Number of equal payments to pay the outstanding balance = 5
So
Payment that has to be made
by the Alvarez family in 5 equal parts = 1500/5 dollars
= 300 dollars
So the Alvarez family has to make 5 payments of $500 to complete the outstanding amount of the car. I hope the procedure is clear enough for you to understand.

Final answer:

After a down payment of $500, the Alvarez family has $1,500 left to pay for a car. They can divide this balance into 5 equal payments of $300 each.

Explanation:

The Alvarez family bought a car for $2,000 and made a down payment of $500. This means that the amount left to pay for the car, also known as the car's balance, is $1,500 ($2,000 minus $500 = $1,500). If the family wants to make 5 equal payments, we will divide that balance by the number of payments they want to make.

So, the calculation would be $1,500 divided by 5, which equals $300. Therefore, each equal payment would have to be $300 for the Alvarez family to pay for the balance of the car over 5 payments.

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Dixon and his little sister Ariadne stand next to each other on the playground on a sunny afternoon. Their mother measures their shadows. Dixon's shadow is 18 feet long and Ariadne's shadow is 15 feet long. If Dixon is 6 feet tall, how tall is Ariadne?

Answers

Ariadne is 5 feet tall because 18 is 6x3 which would mean you would have to divide 15 by three to get the answer which is 5.

She would be 5ft tall because if you set the problem up in a ratio and cross multiple and divide 5 is your answer

2p/6-19=-9 What is p?

Answers

$(2p)/(6)$ - 19 = -9

$(2p)/(6)$ = 10

p = 10 ( $(6)/(2)$

p = 10 (3)

p = 30

Answer: 30

$(2p)/(6) - 19 = - 9 \n (2p)/(6) = 10 \n 2p = 60 \n p = 30$

Please simplify n-2/n^2-4

Answers

Answer:

$\frac{1}{ {n} + {2}}$

Step-by-step explanation:

$\frac{n - 2}{ {n}^(2) - 4} \n \n = \frac{n - 2}{ {n}^(2) - {2}^(2) } \n \n = \frac{n - 2}{ ({n} + {2})({n} - {2})} \n \n = \frac{1}{ {n} + {2}} \n$

Georgia’s gross pay was $35,600 this year. She is to pay a federal income tax of 16%. How much should Georgia pay in federal income tax this year?

Answers

Georgia should pay $5,260.26 federal tax.

I am assuming that Georgia is an employee.

Gross Pay     35,600.00
Deductions:
C.O.L.A
Social Security 6.20% 2,207.20
Medicare 1.45% 516.20 2,723.40
Taxable Income 32,876.60
Federal Income Tax 16%    5,260.26
Net Income    27,616.34

Gross income is different from Taxable Income. There are deductions that must be deducted from gross income to arrive at the taxable income. Deductions such as: Cost of Living Allowances (Social Security, Medicare, Retirement Earnings, other non taxable deductions).

There are also deductions that are subject to tax but not the federal estate tax. They are deductible because the tax for that item has already been paid in another form of tax. If said item is not deducted, then double taxation occurs, meaning the taxpayer paid two kinds of taxes for only one item.

Answer:

$5,696.00

Step-by-step explanation:

This is the correct answer the one before me messed up with the math somewhere.

How do you factor, 45c + 10d?

Answers

We can't factor out a c or d, since we don't know c in terms of d, or vise versa. We thus can only factor out an integer. We see that both numbers are divisible by 5, so we factor out a 5, for a result of 5(9c+2d). 9 and 2 do not have any common factors other than 1, so we have factored fully. Thus, the answer is 5(9c+2d).

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