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
Olegator [25]
3 years ago
9

For f(x)= 3x+1 and g(x)= x^2-6, find (g/f)(x).

Mathematics
2 answers:
o-na [289]3 years ago
4 0
D. The exclusion is important because we cannot divide by zero. Apart from that we are simply looking at a function. 
Anton [14]3 years ago
3 0

Answer:

A. \frac{x^2+6}{3x+1}, x\neq -\frac{1}{3}

Step-by-step explanation:

Given functions,

f(x) = 3x + 1

g(x) = x^2 - 6

∵ (\frac{g}{f})(x) = \frac{g(x)}{f(x)}

By substituting the values,

(\frac{g}{f})(x)=\frac{x^2-6}{3x+1}

Which is a rational function,

We know that,

A rational function is defined for all real numbers except those for which denominator = 0,

If 3x+1 = 0

\implies 3x = -1

\implies x =-\frac{1}{3}

i.e. domain restriction of g/f is x≠ -1/3

Hence, OPTION D is correct.

You might be interested in
The fare for a taxi cab is $2.50 per passenger and $0.75 for each mile. A group of friends has $22.00
xeze [42]

For this case we have to:

x: Let the variable representing the number of people to travel in the group

y: Let the variable representing the number of miles traveled.

If friends only have $22 then we have the following inequality:

2.50x + 0.75y \leq22

Now, if there are three people in the group we have that x = 3.

2.50 (3) + 0.75y \leq22\\7.5 + 0.75y \leq22\\0.75y \leq22-7.5\\0.75y \leq14.5\\y\leq \frac {14.5} {0.75}\\y\leq19.33

The taxi can travel a maximum of 19.33 miles.

On the other hand, if the group wants to travel 10 miles then we have to y = 10.

2.50x + 0.75 (10) \leq22\\2.50x + 7.5 \leq22\\2.50x \leq22-7.5\\2.50x \leq14.5\\x\leq \frac {14.5} {2.50}\\x \leq5.8

Thus, they could travel a maximum of 5 people.

ANswer:

2.50x + 0.75y \leq22

Traveling 3 people, the taxi can travel a maximum of 19.33 miles

Traveling 10 miles, a maximum of 5 people can travel

7 0
3 years ago
Let f(x) = 5x +7 and g(x) = x-1 . Find f(g(x))
Bogdan [553]

Answer:

f(g(x))=5×(x-1)+7=5x-2

6 0
3 years ago
 Mr. Elmore's favorite candy is skittles and his favorite flavor combination is lemon & lime. He has a jar of skittles with
jasenka [17]

Answer:

I'm not really sure but it's 30% yellow and 15% green soo or it is 45% or 15% but idk (i don't know if i helped you but that's what I try to do.

3 0
3 years ago
NEED HELP QUICK!!
sashaice [31]

Answer:

Y = negative x + 9

Step-by-step explanation:

Find the equation of the line for side S-

m= 4-1/1-4 = 3/-3 = -1

<u>The Gradient is -1</u>

Since parallel lines share the same gradient, it should be either of the first two options.

We can see side Q shares the same gradient: 3-6/6-3= -1

Find the equation of the line of side Q-

y-y1= m(x-x1)

y-6= -1(x-3)

y-6=-x+3

<u>y= -x+9</u>

4 0
2 years ago
Read 2 more answers
HELP PLS!!!!<br><br> Find the area of the shape shown below.
Drupady [299]

Answer:

28

Step-by-step explanation:

sorry if wrong

3 0
3 years ago
Other questions:
  • Write the number equal to 2 tens 15 ones
    8·2 answers
  • Jason cut three acres of grass at a farm which is 15 percent of the property how many acres are on the farm
    13·1 answer
  • A rental car company charges $15/day for a rental car plus 20¢ for every mile driven that day. Which equation models the relatio
    7·2 answers
  • Chords AB and CD intersect at point E, AE = 10, EB = 4, and CE = 8. Therefore, ED =
    13·2 answers
  • Steven wants to keep track of how many miles he walks in a year. He expects to walk 5 miles per day, and he has
    9·1 answer
  • A group of 22 students participated in a race. Their scores are below: Score (points) 4–5 6–7 8–9 10–11 12–13 Number of Students
    10·1 answer
  • Last month, mrs. Johnson received a phone bill for $26.86. If the company charges $0.17 per minute l, and there were no other ch
    11·2 answers
  • Х<br> 6<br> -11<br> Find x<br> y<br> 5<br> -5<br> 66<br> -66
    6·1 answer
  • Find the volume please, worth 20 pts I need answers asap:')​
    5·1 answer
  • 30 POINTS NEED HELP ASAP MATH QUESTION<br><br> A. 19<br> B. 108<br> C. 133<br> D. 763
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!