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
pantera1 [17]
3 years ago
13

Determine the domain of the function (fog) (x) where f(x) = 3x-1/x-4 and g(x)=x+1/x

Mathematics
1 answer:
Mrac [35]3 years ago
4 0

Answer:

(-\infty,0)\cup(0, \frac{1}{3})\cup (\frac{1}{3},\infty)

Step-by-step explanation:

The given functions are f(x)=\frac{3x-1}{x-4} and g(x)=\frac{x+1}{x} .

We now composed the two functions to find:

(f\circ g)(x)=f(g(x))

\implies (f\circ g)(x)=f(\frac{x+1}{x})

\implies (f\circ g)(x)=\frac{3(\frac{x+1}{x})+1}{\frac{x+1}{x}-4}

\implies (f\circ g)(x)=\frac{4x+3}{1-3x}

This function is defined if the denominator is not zero.

1-3x\ne0

x\ne\frac{1}{3}

We write this in interval notation as:

(-\infty,\frac{1}{3})\cup (\frac{1}{3},\infty)

We need to be cautious here as x=0 is not in the domain of g(x).

Therefore the domain of (f\circ g)(x) is

(-\infty,0)\cup(0, \frac{1}{3})\cup (\frac{1}{3},\infty)

You might be interested in
Alisa had 1/2 L of juice in a bottle. She drank 3/8 L of her juice. What
Elina [12.6K]

Answer:

3/16

Step-by-step explanation:

By drinking 3/8 liters of 1/2 liter juice it means the question tests the ability to multiply fractions. Since she drank 3/8*1/2=3/16

We multiply the numerators and denominators separately ie 3*1/(8*2)=3/16

Therefore, Alisa consumed 3/16 or 0.1875 or 18.75% of the juice.

Since the question was in fractional form, it is prudent to also express answer in fractions hence the right answer is 3/16

3 0
3 years ago
Help me please, i don’t get it loll
BabaBlast [244]

Answer:

subtract to find A

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
PLEASEEEE HELLP ON A TIMER 15 MINS LEFT
emmainna [20.7K]

Answer: D.

Step-by-step explanation: you find the ratio of the other lengths, then apply that ratio to the length of DC. Pls mark as brainliest?

8 0
2 years ago
An oil tank is leaking into a lake at a rate of 0.1 m3/day. The oil slick forms a semicircular disk whose center is at the leak
gregori [183]

Answer:

17.9  m/s

Step-by-step explanation:

Volume of the slick =  0.5 x π r² h--------------------------------- (1)

Where r = radius of slick

           h = thickness of slick, 10⁻⁶m

If 0.5m³ of oil leaked, then the radius of the semicircular slick can be calculated from equation (1)

V  =  0.5 x π r² h

0.5=  0.5 x  π x  r² x 10⁻⁶

r²   =  10⁶/ π

r =     10³/√π

dV/dt =   πrh dr/dt  + 0.5π r² dh/dt----------------------------------- (2)

Asumming the film thickness is constant , equation (2) becomes

dV/dt =   πrh dr/dt-------------------------------- (3)

dV/dt = 0.1m³/day

r=  10³/√π

dr/dt= rate of expansion of the slick

Substituting  into (3);

0.1 =  π x 10³/√π x 10⁻⁶ x dr/dt

dr/dt = 0.1  x 10⁶/ ( π x 10³/√π)

       =  17.9479 m/s

       ≅  17.9  m/s

8 0
3 years ago
Can someone please help I really need this to be correct.
kupik [55]
I think it’s 22 or 23...I’m so sorry if it’s wrong :/
8 0
3 years ago
Other questions:
  • Is the answer 22.52? If not, what is it?
    15·1 answer
  • Jena and matt, working together, can mow the lawn in 44 hours. working alone, matt takes four times as long as jena. how long do
    12·1 answer
  • The surface area of the triangular prism is .
    14·2 answers
  • Given sets A and B, prove that the following two conditions are equivalent: (1) A \ B = B \ A, (2) A = B.
    13·1 answer
  • If F(x)=3x^2-2 find (-3) x f (x)
    6·2 answers
  • How do you get the answer?
    15·2 answers
  • The slope for , (-2, 5 ) , (2,0 )
    10·2 answers
  • 25 POINTS!! which point is a solution to the inequality shown in this graph 3,-1 -3,-3
    5·1 answer
  • Can you find the perimeter and area of the figure?
    8·2 answers
  • Nina buys a small rug in the shape of a kite. The width of the rug is half its height. What are the width and area of the rug? (
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!