Determine the inverse of the function f (x) = 3(x − 4)^2 + 5.

Answers

Answer 1

Step-by-step explanation:

since g(f(x)) = x g (f (x) )= x, f - 1 (x) = 5x3 + 43 f - 1 (x) = 5 x 3 + 4 3

Answer 2

The inverse of the given function [tex]f(x) = 3(x-4)^{2} +5[/tex] is [tex]f^{-1} (x) = \sqrt{\frac{x-5}{3} } +4[/tex].

What is the inverse of a function?

An inverse function or an anti function is defined as a function, which can reverse into another function. In simple words, if any function “f” takes x to y then, the inverse of “f” will take y to x. If the function is denoted by ‘f’ or ‘F’, then the inverse function is denoted by [tex]f^{-1}[/tex] or [tex]F^{-1}[/tex].

According to the given equation.

We have a function.

[tex]f(x) = 3(x-4)^{2} +5[/tex]

The above function can be written as

[tex]y = 3(x-4)^{2} +5[/tex]

Write the above function for x.

[tex]\implies y -5 = 3(x-4)^{2}[/tex]

[tex]\implies \frac{y-5}{3} = (x-4)^{2}[/tex]

[tex]\implies \sqrt{\frac{y-5}{3} } =x-4[/tex]

[tex]\implies \sqrt{\frac{y-5}{3} } +4=x[/tex]

[tex]0r\ x = \sqrt{\frac{y-5}{3}}+4[/tex]

Replace [tex]x[/tex] by [tex]f^{-1}(x)[/tex] and [tex]y[/tex] by [tex]x[/tex].

We get

[tex]f^{-1} (x) = \sqrt{\frac{x-5}{3} } +4[/tex]

Hence, the inverse of the given function [tex]f(x) = 3(x-4)^{2} +5[/tex] is [tex]f^{-1} (x) = \sqrt{\frac{x-5}{3} } +4[/tex].

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Related Questions

what is 4x+2=-12+6x?????????

Answers

Answer:

x=7

Step-by-step explanation:

What are the y-intercept and the slope of the graph of the
following equation?
-2x + 4y = 8

Answers

-2x + 4y = 8
4y = 2x + 8
y = 1/2x + 2

Y-intercept is (0,2)
Slope = 1/2

Answer:

slope=2/4 or 1/2

Y-Intercept=8

Step-by-step explanation:

-2x+4y=8

+2x both sides

4y=2x+8 /4

y=2/4x+8

Slope=2/4 or 1/2

Y-Intercept=8

Find the perimeter of the triangle.

Answers

Answer:

P

=

a

+

b

+

c

Step-by-step explanation:

The regular price of a baseball hat is $14.45. If Carlos buys the baseball hat on sale for 20% off the regular price, how much change will he receive after paying with $20? No links!

Answers

Answer:

I believe it's $8.44 hope this helps

ill mark brainliest

A figure that undergoes a translation, reflection, or rotation will result in a figure that is _______ to the original. The symbol used is ≅.

Answers

Awnser: Hi, tour awnser is Congruent

This rectangular prism was built with cubes that each have a volume of one cubic centimeter.

What is the volume of the rectangular prism?

Answers

Answer:

The volume of this rectangular prism is 60.

Step-by-step explanation:

V = L*W*H

( For a rectangular prism )

4 * 5 * 3

Answer:

To find the volume of a rectangular prism, multiply its 3 dimensions: length x width x height. The volume is expressed in cubic units.

ppls answer correct for a brainliest answer and points.

Answers

Answer:

12y + 2y² or 2y² + 12y

Step-by-step explanation:

4(2y + 3y) becomes 8y + 12y:

4 × 2y = 8y4 × 3y = 12y

y(2y - 8) becomes 2y² - 8y:

y × 2y = 2y²y × -8 = -8y

8y + 12y + 2y² - 8y = 12y + 2y² (the 8y's cancel out)

Answer: 12y + 2y² or 2y² + 12y

Hope this helps!

Anyone, please answer this question

Answers

Answer:

The answer is A.

Step-by-step explanation:

they equal the same amount

Use the given frequency table to find mean, median,mode,and range.

Answers

Answer:

Mode:6

median: 5.5

mean: 5.25

range : 2

Step-by-step explanation:

Evaluate the expression x-7, if x= 12. 19 6 05. (please help :( )​

Answers

Answer:

the answer is 5...............

Answer:

[tex]5[/tex]

Step-by-step explanation:

[tex]\sf x-7[/tex]

[tex]\sf x=12[/tex]

→ [tex]\sf (12)-7[/tex]

→ [tex]\sf 5[/tex]

Sweaters a Target have an original price of $28. Spring is coming so Target puts those sweaters on sale fo $21.

What is the discount amount? $


What is the percent of discount?

Answers

Answer:

7 & 75%

Step-by-step explanation:

28 - 21 = 7

Discount amount - 7

Find the percent of discount now:

21:28*100 =

(21*100):28 =

2100:28 = 75

1)The discount amount is $7
2)25% off

There is a raffle at a hockey game and 125 tickets are sold. Maris bought 3 tickets. What percent of the tickets
does Maris have?

Answers

Answer:

2.4%

Step-by-step explanation:

Answer:

2.4 percent

Step-by-step explanation:

write the equation of the line perpendicular to the given line y - 2 = 1/4 (x+2)

Answers

When a line is perpendicular the slope is the negative reciprocal. Here it would be -4. The you plug in the points they have you and get y - 5 = -4(x - 2)

6a) find the value of x in the following proportions. a) 3:5=12:x b) 4:3=20:x c) 5:6=x:12 d) 7:2=x:6​

Answers

Answer:

A. x = 20

B.x = 15

C. x = 10

D. x = 21

Step-by-step explanation:

In pic they are in order

(Credit: Symbolab)

(Hope this helps can I pls have brainlist (crown)☺️)

You’ve decided to open a checking account. You know there are a number of differences with individual banking institutions. Name at least 3 good questions to ask to get started, and explain why knowing this information is helpful. Use complete sentences.

Answers

Answer:

1. Can I use the Atm for free?

2. What happens if I withdraw more money than I have in my account?

3. Does my account pay me intrest?

Step-by-step explanation:

1.ATMs allow you to withdraw money from your checking account without visiting a bank branch. But some withdrawals could cost you. Many banks charge you to use machines operated by other banks or third parties, and those fees can add up quickly.

2. Withdrawing more than your account contains is called an overdraft. Bank overdraft services generally allow your transaction to go through, but you will be charged a fee. Some banks prevent you from overdrafting when swiping your debit card and may let you request that all transactions are declined when your account doesn’t contain enough funds.

3. Generally, if checking accounts pay interest, the rate is very low. High-yield checking accounts offer higher interest but typically require higher balances. Savings accounts offer higher rates, but because the accounts are intended for saving, they’re subject to different rules

8xy + 14x + 4x - 2xy + 6y
I NEED HELP ON IT

Answers

Answer:

Welp i dont have your help you need

Step-by-step explanation:

Because i just dont

HELP PLEASEEEEEEE!!!!

Answers

Step-by-step explanation:

answer/ explanation is in the picture

Answer:

2.02units

Step-by-step explanation:

tan68°=[tex]\frac{5}{x}[/tex]=2.4750868534163,so x ≈2

Can someone please show me y=2x-2 and x=4 on a graph please. ( IF U CAN PLEASE SHOW ME WHERE THE LINES GO THROUGH EACH OTHER ON A GRAPH)

Answers

Here is the graph. Work is shown in the picture. I hope this helps.

divide -3 1/3 by 1 1/5

Answers

-2/3 is the answer
Decimal form: -0.6

Identify the slope and y-intercept of the line y = 9x - 3

Answers

Answer:

slope = 9 , y- intercept = - 3

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 9x - 3 ← is in slope- intercept form

with slope m = 9 and y- intercept c = - 3

Solve UV,RS,RT Please And Thank You

Answers

Answer:

⬇️

Step-by-step explanation:

UV = 1/2 TS

UV = 1/2 42

UV = 21

RS = 2* UW

RS = 2*23

RS = 46

RT = 2 * VW

RT = 2*19

RT = 38

Perimeter of RST = RT + TS + RS

Perimeter of RST = 38 + 42 + 46

Perimeter of RST = 128

help yall

Solve and graph the absolute value inequality: 2x + 1) 5.

Answers

Answer:

x=2

Step-by-step explanation:

2x=5-1

2x=4

x=4/2

simplify 4/2 to 2, x=2

Answer:

B is the answer

The inequality is −

3≤x≤2

Step-by-step explanation:

The expression - 250 + 16z represents a submarine that began at a depth of 250 feet below sea level
and ascended at a rate of 16 feet per minute. What was the depth of the submarine after 9 minutes?

Answers

= -250 + 16z
= -250 + 16(9)
= -250 + 144
= -106 feet

In football, the path that a defender must run to tackle the ball carrier is called the path of pursuit. If the ball carrier runs 40 yards to the end zone and the path of pursuit is 45 yards, how far apart were the ball carrier and defender when they started? Answer with appropriate precision. (Hint: Use the Pythagorean Theorem.)

Answers

Answer:

Step-by-step explanation:

The ball carrier and defender were 20.62 ft apart

Let the path the ball carrier runs = x and y = path of pursuit and L = distance between defender and ball carrier when they started.

x, L and y form a right angled triangle with y being the hypotenuse side of the triangle.

From Pythagoras' theorem,

x² + L² = y²

So, L² = y² - x²

L = √(y² - x²)

Since x = 40 yards and y = 45 yards,

#substituting the values of the variables into the equation, we have

L = √(y² - x²)

L = √(45² - 40²)

L = √(2025 - 1600)

L = √425

L = 20.62 ft

So, the ball carrier and defender were 20.62 ft apart

Learn more about Pythagoras' theorem here:

https://brainly.com/question/23713139

OMG PLS HELP ME N ANSWER

Answers

it is the second one or B

Answer:

Step-by-step explanation:

In mathematics, a function is any expression that produces exactly one answer for any given number that you give it. The input is the number you feed into the expression, and the output is what you get after the look-up work or calculations are finished.

So I believe B.

solve 4(2x-5)=5x+4 pls​

Answers

Answer:

x=8

Step-by-step explanation:

4(2x-5)=5x+4

Distribute

8x -20 = 5x+4

Subtract 5x from each side

8x -20 -5x = 5x+4-5x

3x-20 = 4

Add 20 to each side

3x-20+20 = 4+20

3x = 24

Divide by 3

3x/3 =24/3

x=8

Can someone help me with number 5 :((

Answers

the answer is 83
a10=11+(10-1)8

Your aunt loves to bake cookies she is planning on opening a bakery she usually makes 50 cookies for a small family gatherings your aunt wants to bake 10 times as many cookies for her grand opening how many cookies will your need to bake

Answers

Answer:

500=10x50

Step-by-step explanation:

Suppose f(x) = 3x*2 - 2x

Find f(-4)

Answers

Answer:

f(- 4) = 56

Step-by-step explanation:

Substitute x = - 4 into f(x) , that is

f(- 4) = 3(- 4)² - 2(- 4) = 3(16) + 8 = 48 + 8 = 56

Which graph represents the table only A or B

Answers

Show a clear picture
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