1) Find the inverse function of f(x)=1/2x+32)Use composition to verify that they are inverse relations?
3) f^ Domain : Range:
4) f^-1 Domain : Range:

Answers

Answer 1

Answer: y = 1/2x + 3
change x and y

x = 1/2y + 3
now find the value of y and that is inverse function

x - 3 =1/2 y
y = 2x- 6

f-(x) = 2x - 6

for both domain : ( - ∞ , + ∞ )

range f (x) : ( - ∞ , + ∞ ) - { 0 }
range f-(x) :( -∞ , +∞)

Answer 2

Answer: To find the inverse function you need to change $f(x)$ (call it $y$ ) and $x$ , then solve for $y$ :

$y = (1)/(2)x+3 \n x = (1)/(2)y + 3 \n x - 3 = (1)/(2)y \n 2x-6 = y$

So now you have $f^(-1)(x) = 2x-6$ .

Composition to prove inverse relation: $f \circ f^(-1) (x) = x$ :

$f(f^(-1)(x)) = (1)/(2)(2x-6)+3 = x - 3 + 3 = x \square$

Domain and Range of both functions is Real numbers since they are both linear equations.

Related Questions

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Which situation could be modeled by using a linear function ?1) a bank account balance that grows at a rate of 5% per year compounded annually 2) a population of bacteria that doubles every 4.5 hours 3) the cost of the cell phone service that charges a base amount plus 20 cents per minute 3) the concentration of medicine in a persons body that decays by a factor of one- third every hour
The sum of the age of two sisters is 20 years. If the one of them is 4 years younger than other , find their age.
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Substitute the given values into the formula, and solve for the unknown variable.1A= 2h(B+b); A=44, B = 2, b= 9h=

Javier has a job installing windows. He earns a rate of $75 per day plus $8 per window installed. He also receives a stipend of $25 for snacks. Javier knows his weekly earnings can be shown with the following expression:75d + 8w + 25

Part A: Identify a coefficient, a variable, and a constant in this expression. (3 points)

Part B: If Javier works for 5 days and installs 48 windows, how much does he earn? Show your work to receive full credit. (4 points)

Part C: If Javier gets an increase in his stipend and receives $40 for snacks, would the coefficient, variable, or constant in the equation change? Why? (3 points)

Answers

Part B is 784
75 multiplied by 5 is 375
8 multiplied by 48 is 384
375 plus 384 is 759
759 plus 25 is 784

Which number sentence shows the correct placement of the decimal point in the product, based on the two factors?3.48 × 42.37 = 147.4476
23.2 × 8.8 = 20.416
0.39 × 7.2 = 28.08
43.72 × 9.2 = 4,022.24

Answers

3.48 × 42.27 = 147.4476

Yes he is right it is A

Jess observed that 60% of the people at a mall on a particular day shopped for clothes. If 2500 people at the mall did not shop for clothes that day, the number of people who shopped for clothes that day was ______. (only put numeric values, no other symbols)

Answers

The 2500 people that did not shop for clothes that day accounts for 40% of the total people present in the mall. The total number of people present at the mall that day is the quotient obtained when 2500 is divided by 40% which is 6250. Since the number of people who shopped for clothes that day is 60% of the total number of people, multiply 6250 by 60%. This gives an answer of 3750.

Therefore, there are 3750 people who shopped for clothes that day.

Answer:

3750

Step-by-step explanation:

What is an equation of the line that is perpendicular to y + 1 = -3(x - 5) and passes through the point (4, -6)?

Answers

Answer:

Option A.

Step-by-step explanation:

y + 1 = -3x + 15

y = -3x + 14

A line perpendicular would have a slope of 1/3.

y = 1/3x + c

-6 = 1/3 * 4 + c

4/3 + c = -6

c = -18/3 - 4/3

c = -22/3

So, we have y = 1/3x - 22/3.

y + 6 = 1/3(x - 4)

y + 6 = 1/3x - 4/3

y = 1/3x - 4/3 - 18/3

y = 1/3x - 22/3

So, the correct answer is Option A.

Hope this helps!

A printer printed 68 letters in 4 seconds. If it prints letters at a constant speed, it can print ______ letters in 30 seconds.

Answers

510 letters. 68/4=17 which means 17 letters per second. You are trying to find out how many letters you can do in 30 seconds, so you just simply multiply 17 by 30 to get 510 letters. Hope this helped!

The answer is 510, Im glad I can help! Enjoy the test!

Candy draws a square design with a side length of x inches for the window at the pet shop. She takes the design to the printer and asks for a sign that has an area of 16x2 – 40x + 25 square inches. What is the side length, in inches, of the pet shop sign? 4x + 5 4x – 5 8x + 5 8x – 5

Answers

The pet shop sign is modelled as a square. The area of the square is given as $16x^(2)-40x+25$ .

Technically we want to take a square root of this expression to find the length of one side of the square but we will check first whether factorising will give us equal roots

$16x^(2)-40x+25$
$16 x^(2) -20x-20x+25$
$4x(4x-5)-5(4x-5)$
$(4x-5)(4x-5)$

As we see that by factorising gives us $(4x-5)^(2)$ hence the side length of the square is $4x-5$