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
Mars2501 [29]
3 years ago
7

Inverse of the function f(x)=4x

Mathematics
2 answers:
KatRina [158]3 years ago
6 0

Answer:

\large\boxed{f^{-1}(x)=\dfrac{1}{4}x}

Step-by-step explanation:

f(x)=4x\to y=4x\\\\\text{exchange x to y and vice versa:}\\\\x=4y\qquad\text{solve for}\ y:\\\\4y=x\qquad\text{divide both sides by 4}\\\\y=\dfrac{x}{4}=\dfrac{1}{4}x

Pani-rosa [81]3 years ago
4 0

Answer:

f(x)^-1 = x/4

Step-by-step explanation:

f(x)=4x

inverse

x = 4y

rewrite

4y = x

y = x/4

Answer:

f(x)^-1 = x/4

You might be interested in
Suppose it takes 18 hours for a pipe to fill a tank of water, if the tank
Lemur [1.5K]

Answer:

Step-by-step explanation:

Let the volume of tank be x

In 18 hours volume of tank filled = x

we have to find the volume of tank which is filled in 1 hours.

For that we divide LHS and RHS by 18

In 18/18 hours volume of tank filled = x/18

In 1 hours volume of tank filled = x/18

In 30 hours volume of tank emptied = x

we have to find the volume of tank which is emptied in 1 hours.

For that we divide LHS and RHS by 30

in 30/30 hours volume of tank filled = x/30

In 1 hours volume of tank filled = x/30

If tank is empty and one starts to fill it, two things will happen

it will start filling at rate of x/18 hours

But there is leak which will start to empty the tank at  x/30 hours

So , at any given time rate if filling of water will be rate of filling the tank- rate of emptying the tank

In 1 hour volume of tank filled if both filling and leaking takes place simultaneously =  x/18 -x/30 = (30-18)x/18*30 = 12x/18*30 = x/3*15 = x/45

In 1 hour volume of tank filled = x/45

in 1*45 hour volume of tank filled = x/45*45 = x

Thus, it will take 45 hours to fill the leaky tank  .

4 0
3 years ago
Prince Ivan rides gray wolf and a constant speed from kings castle to the magic apple garden in five hours. on the return trip t
borishaifa [10]

Answer:

The original speed of the grey wolf can be 9 and/or 48 km/hour

Step-by-step explanation:

There are two trips. One to King Castle (KC) to Magic Apple Garden (MAG), and then back (MAG - KC).

First trip: KC - MAG

It takes the same distance as MAG - KC so distance can be D for both.

Then it is stated that it takes 5 hours or 300mins for him to go from KC - MAG, and the speed is constant.

Let x be speed.

So the equation for this is:

D=5x

Second trip: MAG - KC

Here he goes 36 mi at constant speed (x), then picks up his speed by 3 km/hour (x+3).

For Time:

He reaches to KC, 15 mins earlier than KC - MAG, so he reaches there in 4.75 hours or in 275 min.

The problem splits into two as there are two different times, for the two parts of the journey or distance for MAG - KC.

Let T#1 = a, and T#2 = b.

Let D#2 = D-36

The equation for a:

a = 36/x --> This is he is at a constant speed and went for 36mi.

Next:

The equation for b:

b = (x+3)/D#2

These two equation have to be added as (a+b) = 4.75 --> 4.75 is the total time for MAG - KC.

So the equation is:

36/x + (5x-36)/x+3 = 4.75 --> Knowing (a+b) = 4.75, just put 4.75 as the equal, and add the fractions that equal (a) and (b).

Now Solve:

36/x + (5x-36)/x+3 = 4.75

0.25s^2 + 108 + 5s^2 - 36s = 4.75s*(s+3)

0.25s^2 - 14.25s + 108 = 0

(14.25 +- Square root (203.06 - 108))/0.5

(14.25 +- Square root (95.0625))/0.5

(14.25 +- 9.75)/0.5

Answer:

s = 9, s=48.

Therefore the original speed of the grey wolf can be 9 and/or 48 km/hour.

8 0
2 years ago
1 of 5
timofeeve [1]

Answer:20 girls

Step-by-step explanation:the difference between 3 and 4 is one so there will be a difference of one between the 2 questions.

5 0
3 years ago
In ABC, BC=4 cm, angle b=angle c, and angle a=20 degrees, what is ac to two decimal places
zubka84 [21]

Answer:

Therefore,

AC=11.52\ cm

Step-by-step explanation:

Given:

In ΔABC, BC=4 cm,

angle b=angle c, and

angle a=20°

To Find:;

AC = ?

Solution:

Triangle sum property:

In a Triangle sum of the measures of all the angles of a triangle is 180°.

\angle a+\angle b+\angle c=180\\\therefore 2m\angle b =180-20=160\\m\angle b=\dfrac{160}{2}=80\°

We know in a Triangle Sine Rule Says that,  

In Δ ABC,

\dfrac{a}{\sin A}= \dfrac{b}{\sin b}= \dfrac{c}{\sin C}

substituting the given values we get

\dfrac{BC}{\sin a}= \dfrac{AC}{\sin b}

\dfrac{4}{\sin 20}= \dfrac{AC}{\sin 80}\\\\AC=11.517=11.52\ cm

Therefore,

AC=11.52\ cm

8 0
3 years ago
Read 2 more answers
If the quadrilateral below is a rectangle, find the missing measures. Round to one decimal place.
Katarina [22]

Answer:

Quad=4 so you need to round it off

3 0
2 years ago
Other questions:
  • Which is the length of the hypotenuse, x, if (12,35,x) is a Pythagorean triple
    11·1 answer
  • A person on tour has dollar 360 for his daily expenses. If he extends his tour for 4 days, he has to cut down his daily expenses
    6·1 answer
  • Help someone!! Thank you (:
    12·1 answer
  • God Bless u plz help plz bless ur grades
    14·1 answer
  • Factor 2x 2 - 10x - 12.
    11·2 answers
  • Omar has a gift card for $40.00 at a gift shop. Omar wants to buy a hat for himself for $13.50. For his friends, he would like t
    12·2 answers
  • Find the area. 14 m 4.5 m 4.5 m 9m 12 m 3 m 3 m <br><br>plzzz help meeee​
    9·1 answer
  • The circumference of the circle was 12π , what is the radius
    8·2 answers
  • Help plzzzzzzzzzzzzzzzzz
    8·1 answer
  • A right triangular prism is shown.What is the lateral surface area?
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!