1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Rashid [163]
2 years ago
5

The graph of f(x) is shown below.

Mathematics
1 answer:
Simora [160]2 years ago
4 0

The intersection would be at the point (2, 2).

This is because, graphically, the plots of f(x) and its inverse are reflections of one another across the line y = x, and (2, 2) lies on this line.

Put another way, we have f(2) = 2 = f⁻¹(2), so both f(x) and f⁻¹(x) intersect when x = 2.

Put yet another (longer) way, we can find the equation for f(x): it's a line that passes through (0, 6) and (3, 0), so it has slope -6/3 = -2. Then using the point-slope formula,

y - 6 = -2 (x - 0)   ⇒   y = f(x) = -2x + 6

By definition of function inverse, we have

f(f⁻¹(x)) = x

so that with the given definition of f(x), we get

f(f⁻¹(x)) = -2 f⁻¹(x) + 6 = x

-2 f⁻¹(x) = x - 6

f⁻¹(x) = -x/2 + 3

Then we solve for x such that f(x) = f⁻¹(x). We would find x = 2 as before.

You might be interested in
NEED HELP ASAP!!!!!!!!!!!
Arte-miy333 [17]

Answer:

Step-by-step explanation:

Let the no of cars be x and no of buses be y.

x + y = 60 -> y = 60 - x

6x + 30y = 600

with the available equations let us calculate the values of x and y.

6x + 30 * (60-x) = 600

6x + 1800 - 30x = 600

24x = 1200

x cars = 50

y buses = 10

maximum profit = 50 * 2.5 + 10 * 7.5 = $200

5 0
3 years ago
the most a bowling ball can weigh is 7,258 grams. what is the most it can weigh when measured in pounds? explains plz
konstantin123 [22]
16 pounds because 7258 grams goes into 16.001
6 0
3 years ago
The distribution of individual incomes in the United States is strongly skewed to the right. In 2013, the mean and median income
vesna_86 [32]

Answer:

The mean would be $322,343 and the median would be $196,723.

Step-by-step explanation:

Since the distribution of individual incomes is skewed to the right, it means that the distribution has a long right tail.

Drawing a distribution with this characteristic, we can see how the majority of the data falls into the left side of the graphic, meaning that a lot of people receive less income. Following this reasoning, the mean which is the amount of the data (in this case individual income) divided by the amount of people, would be the higher number, meaning that the few people who earn more money would influence in making this number higher.

Following this reasoning, the median (which is not influenced by this difference) would be the less high number.

5 0
3 years ago
What is the solution to the equation t-15=76
geniusboy [140]

Answer:

T = 91

Step-by-step explanation:

Simplifying

T + -15 = 76

Reorder the terms:

-15 + T = 76

Solving

-15 + T = 76

Solving for variable 'T'.

Move all terms containing T to the left, all other terms to the right.

Add '15' to each side of the equation.

-15 + 15 + T = 76 + 15

Combine like terms: -15 + 15 = 0

0 + T = 76 + 15

T = 76 + 15

Combine like terms: 76 + 15 = 91

T = 91

Simplifying

T = 91

3 0
2 years ago
Read 2 more answers
Question 1 (Essay Worth 10 points) (01.02 MC) Part A: If (26)x = 1, what is the value of x? Explain your answer. (5 points) Part
katen-ka-za [31]

Answer:

See Explanation

Step-by-step explanation:

The question is not clear. However, I will treat the question as:

(26)x = 1

(50)x = 1

and:

(2^6)^x = 1

(5^0)^x = 1

Solving: (26)x = 1  and  (50)x = 1

(26)x = 1

Divide both sides by 26

x = \frac{1}{26}

(50)x = 1

Divide both sides by 50

x = \frac{1}{50}

Solving (2^6)^x = 1 and (5^0)^x = 1

(2^6)^x = 1

Express 1 as 2^0

(2^6)^x = 2^0

Remove bracket

2^{6x} = 2^0

Cancel out 2

6x = 0

Divide both sides by 6

x = \frac{0}{6}

x = 0

(5^0)^x = 1

Express 1 as 5^0

(5^0)^x = 5^0

Cancel out 5^0

x = 1

8 0
3 years ago
Other questions:
  • Divide. Reduce the answer to lowest terms. 3/4 ÷ 1/3
    11·1 answer
  • If n = 37 cm and l = 12 cm, what is the length of m?
    12·1 answer
  • N is an integer greater than 1.
    7·1 answer
  • Read the following statements. 1. Each of the two items that Val bought cost more than $10. 2. Val spent $34 for the two items.
    11·1 answer
  • What is the correct answer to 14-8=2+
    9·1 answer
  • Что-больше 20% или 1/5
    8·1 answer
  • Write an equation in point-slope form for the line that passes through (–2, 1) with a slope of 1/4. Giving brainliest!
    7·1 answer
  • Pls help pls/plz/plx
    5·2 answers
  • A tutor charges $5 for each class he takes per day that lasts for an hour. for each additional hour he tutors he charges $3. mat
    11·1 answer
  • 164 hundreds - 12 hundreds
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!