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
ruslelena [56]
2 years ago
6

Find f(g(x)). State the domain of the composite function. f(x) = 3x-2/x+1 g(x) = x+5/2x-3

Mathematics
1 answer:
AnnyKZ [126]2 years ago
7 0

Answer:

ℝ - {(-2/3),(3/2)}

Step-by-step explanation:

We want the domain of f(g(x)). So, firstly, we have to find the domain for g(x) and, then, for f(g(x)).

- Domain of g(x): Since the expression is a fracion, we must exclude the values of x that make null the denominator. Hence,

g(x)=\dfrac{x+5}{2x-3}\Longrightarrow 2x-3\neq 0\iff \boxed{x\neq\dfrac{3}{2}}

- Domain of f(g(x)): We'll find its expression:

f(x) = \dfrac{3x-2}{x+1}\\\\f(g(x)) = \dfrac{3g(x)-2}{g(x)+1}\\\\f(g(x)) = \dfrac{3\cdot\dfrac{x+5}{2x-3}-2}{\dfrac{x+5}{2x-3}+1}=\dfrac{~~~\dfrac{3(x+5)-2(2x-3)}{2x-3}~~~}{\dfrac{(x+5)+(2x-3)}{2x-3}}\\\\f(g(x)) =\dfrac{3(x+5)-2(2x-3)}{(x+5)+(2x-3)}=\dfrac{3x+15-4x+6}{x+5+2x-3}\\\\\boxed{f(g(x)) =\dfrac{21-x}{3x+2}}

Now, once again, we have to exclude the values of x that make the denominator equals to zero. Thus,

f(g(x)) =\dfrac{21-x}{3x+2}\Longrightarrow 3x+2\neq0\iff \boxed{x\neq-\dfrac{2}{3}}

Lastly, we may write the domanin of f(g(x)):

D(f(g(x)) = \left]-\infty,-\dfrac{2}{3}\right[\cup\left]-\dfrac{2}{3},\dfrac{3}{2}\right[\cup\left]\dfrac{3}{2},\infty\right[

or, just writing in a shorter way:

\boxed{D(f(g(x)) = \mathbb{R}-\left\{-\dfrac{2}{3},\dfrac{3}{2}\right\}}

You might be interested in
If a toy is 420$ and it is 69% off, how much is it
salantis [7]

Answer:

130.2

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
An airplane flying at a velocity of 610 m/s lands and comes to a complete stop
Len [333]

A) The airplane slowed down. It states that the plane lands and come to a complete stop over a 53 second period.

B) It decelerates. The speed doesn't increase. It slows down.

C) The answer should be positive. Although the deceleration is slowing down the plane, it's not going at a negative speed.

D) The answer is 11.5m/s. I divided the velocity by the amount of seconds it takes to make a complete stop.

3 0
3 years ago
Find the slope of each line then tell what the slope represents
morpeh [17]
1. find slope
x=tickets sold
y=money made
slope=(y2-y1)/(x2-x1)
take any point
(5,23.75) and (10,47.50)
input (note, (x,y))
(47.50-23.75)/(10-5)=23.75/5=4.75
slope=4.75
y=mx+b
m=slope
b=yintercept
y=4.75x+b
input
47.5=4.75(10)+b
47.5=47.5+b
b=0

equation is y=4.75x
if ticket sold is 24 then x=24
y=4.75(24)
y=114
answer is $114

2. points
(0,56.00) and (3,45.5)
slope=(y2-y1)/(x2-x1)
slope=(45.5-56.00)/(3-0)=-3.5
y=-3.5x
slope=-3.5
logic it yourself
equation is
y=-3.5x+0
y intercept is when x=0 so when the start of it was or when time=0
x intercept is when y=0 is when he has no money left





1.a. rate of change=4.75
   b. $114

2. a.do this yourself, (desmos graphing calculator)
   b. slope=-3.5 (duh, means money goes down with time)
   c. equaiton is y=-3.5x+0, xint meanss when he has no money, y int means when time=0 or when it started
3 0
3 years ago
M is directly proportional to r³ when r=4, m=160.work out the value of r when m=20
11Alexandr11 [23.1K]
Die haben sich auch schon in den nächsten Jahren und in den letzten Wochen nicht so viel 5=5
7 0
2 years ago
A cereal box has a length of 8 inches, a width of 2 inches and a height of 12 inches. What is the volume of the cereal box?
DochEvi [55]

Answer:

192 in cubed

Step-by-step explanation:

Multiply 12*2= 24*8

6 0
3 years ago
Read 2 more answers
Other questions:
  • What is 10 divide by 64
    12·1 answer
  • The temperature at noon is -4 degrees Celsius. The temperature at 6:00pm is -12 degrees Celsius. What is the difference between
    9·1 answer
  • Rachel and Sam stopped at the donut stop before work. Rachel bought a protein smoothie and 2 boxes of donut holes for $11.65. Sa
    12·1 answer
  • Please help. Thank youuuuu
    14·1 answer
  • PLZ HELP ME!!!!!! ASAP!! PLZ EXPLAIN YOUR ANSWERS THOROUGHLY!! giving 20 points
    14·1 answer
  • The polygon below is a regular hexagon. What is the approximate length of the apothem? Round to the nearest tenth.
    11·2 answers
  • PLEASE HELP I NEED HELP
    8·1 answer
  • 1. Is a triangle with side lengths 6, 4, 3 a right triangle? Why or why<br> not?
    7·1 answer
  • Of 20 test​ scores, four are less than or equal to 85. What is the percentile rank of a test score of ​85
    12·1 answer
  • A bag of sweets contains mints and toffees only.There are 21 mints in the bag.One quarter of the sweets are toffees.Calculate th
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!