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vekshin1
3 years ago
14

Given that f(x)=2x/3 evaluate f^-1(6)

Mathematics
1 answer:
abruzzese [7]3 years ago
4 0

Answer:

9

Step-by-step explanation:

we know by definition that

f^{-1}(f(x))=x\\\\f^{-1}(\frac{2x}{3})=x\\\\f^{-1}(x)=ax\\\\f^{-1}(\frac{2x}{3})=a(\frac{2x}{3})=x\\\\f^{-1}(x)=\frac{3x}{2}

so now we evaluate

f^{-1}(6)=\frac{3*6}{2}\\\\=3*3\\\\f^{-1}(6)=9

and if we want to do an extra step

f^{-1}(f(6))=6\\\\f^{-1}(\frac{2*6}{3})=f^{-1}(4)=\frac{3*4}{2}=6

which works.

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Find the final cost to the employer.
Lena [83]
The correct answer is A) $75.85.

A discount of 20% means that the cost is 80% of the original.  80%=80/100=0.8

0.8(129) = 103.20

A discount of 30% means that the cost is 70% of the amount before discount.  70%=70/100=0.7
0.7(103.20) = 72.24

A sales tax of 5% means that it is 105% of the amount pre-tax.  105%=105/100=1.05
1.05(72.24) ≈ 75.85
8 0
3 years ago
A pedestal for a statue is made with 405 cubic feet of concrete. a rectangular prism with a height of 9 feet. what is the area o
enyata [817]

45 square feet is the area of the base of the pedestal.

what is rectangular prism?

  • A rectangular prism is a 3D figure with 6 rectangular faces.
  • To find the volume of a rectangular prism, multiply its 3 dimensions: length x width x height. The volume is expressed in cubic units.

we know that

The volume of the pedestal (rectangular prism) is given by the formula

   V =   B × h

where

B is the area of the rectangular base of pedestal

V = 405 ft³

h = 9 ft

put the given values in the formula and solve for B

405 = B × 9

B = 405/9

B = 45 ft²

Therefore, 45 square feet is the area of the base of the pedestal.

Learn more about rectangular prism

brainly.com/question/21308574

#SPJ4

3 0
2 years ago
Which coordinate plane shows the graph of f(x)=2x+3?
andreev551 [17]

Answer:

NOT the graph A and the graph B.

Step-by-step explanation:

y = mx + b

m - slope

b - y-integer

If m > 0 then the function is increasing.

if m < 0 then the function is decreasing.

We have y = -2x + 3

m = -2 < 0 the function is decreasing

b = 3 y-intercept = 3

The x-intercept: y = 0. Substitute

0 = -2x + 3     add 2x to both sides

2x = 3    divide both sides by 2

x = 1.5

Therefore your answer is C or D (look at the picture)

3 0
4 years ago
Mario made 6 snowballs. Jordan made 4 snowballs. How many more snowballs did Mario make than Jordan.
ozzi

Answer:

Mario made 2 more snowballs than Jordan

Step-by-step explanation:

To find you're answer, subtract the amount of snowballs Mario has (6) to the snowballs Jordan has (4).

6-4=2


Hope it helps!

4 0
3 years ago
Ms. Johnson owns a cabinet business that installs cabinets in kitchens. Her employees can install 2/3 of a
atroni [7]

Answer:

10/3 of a kitchen cabinet

Step-by-step explanation:

To make a full hour, 1/5 would be multiplied by 5- and so would their progress.

2/3 * 5 = 10/3, which is also an improper fraction.

6 0
3 years ago
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