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
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].
Find out more information about the inverse of the function here:
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Can someone help me with number 5 :((
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 ≅.
Awnser: Hi, tour awnser is Congruent
what is 4x+2=-12+6x?????????
Answer:
x=7
Step-by-step explanation:
Solve UV,RS,RT Please And Thank You
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
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
Answer:
500=10x50
Step-by-step explanation:
This rectangular prism was built with cubes that each have a volume of one cubic centimeter.
What is the volume of the rectangular prism?
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.
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)
8xy + 14x + 4x - 2xy + 6y
I NEED HELP ON IT
Answer:
Welp i dont have your help you need
Step-by-step explanation:
Because i just dont
solve 4(2x-5)=5x+4 pls
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
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?
ppls answer correct for a brainliest answer and points.
Answer:
12y + 2y² or 2y² + 12y
Step-by-step explanation:
4(2y + 3y) becomes 8y + 12y:
4 × 2y = 8y4 × 3y = 12yy(2y - 8) becomes 2y² - 8y:
y × 2y = 2y²y × -8 = -8y8y + 12y + 2y² - 8y = 12y + 2y² (the 8y's cancel out)
Answer: 12y + 2y² or 2y² + 12y
Hope this helps!
What are the y-intercept and the slope of the graph of the
following equation?
-2x + 4y = 8
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
HELP PLEASEEEEEEE!!!!
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
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?
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
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.)
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:
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Which graph represents the table only A or B
divide -3 1/3 by 1 1/5
Identify the slope and y-intercept of the line y = 9x - 3
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
help yall
Solve and graph the absolute value inequality: 2x + 1) 5.
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 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!
Answer:
I believe it's $8.44 hope this helps
Suppose f(x) = 3x*2 - 2x
Find f(-4)
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
Use the given frequency table to find mean, median,mode,and range.
Answer:
Mode:6
median: 5.5
mean: 5.25
range : 2
Step-by-step explanation:
OMG PLS HELP ME N ANSWER
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.
Evaluate the expression x-7, if x= 12. 19 6 05. (please help :( )
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]
Find the perimeter of the triangle.
Answer:
P
=
a
+
b
+
c
Step-by-step explanation:
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
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)☺️)
write the equation of the line perpendicular to the given line y - 2 = 1/4 (x+2)
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.
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
Anyone, please answer this question
Answer:
The answer is A.
Step-by-step explanation:
they equal the same amount
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?
Answer:
2.4%
Step-by-step explanation:
Answer:
2.4 percent
Step-by-step explanation: