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
saul85 [17]
10 months ago
11

Determine the domain and range of (g ○ f)(x) if f of x is equal to 4 over the quantity x squared minus 4 end quantity and g(x) =

x + 2.
Mathematics
1 answer:
RUDIKE [14]10 months ago
6 0

For the function (gof)(x) the Domain is {x∈ R| ,x ≠ –2, 2} , the Range is {(–∞, 1)∪(2, ∞)} .

In the question ,

it is given that

the function f(x) is given as "4 over the quantity x squared minus 4" ,

which means

f(x)=4/(x²-4)

and g(x)=x+2

we know ,

(gof)(x) = g(f(x))= f(x) + 2

= 4/(x²-4) + 2

taking LCM as (x²-4) and solving further ,

we get

= \frac{4+2x^{2} -8}{x^{2} -4}

= (2x²-4)/(x²-4)

the fraction is defined only when the denominator is non zero,

So for Domain

x²-4 ≠ 0

x² ≠ 4

x ≠ +2,-2

So, the domain is all real numbers except the numbers 2,-2 .

For Range , the graph of the function (gof)(x) is plotted below ,

From the graph we can see that the function does not have any value from y=1 to 2 .

So, the Range will be R={(∞, 1)∪(2, ∞)}.

Therefore , for the function (gof)(x) ,the Domain is {x∈ R| ,x ≠ –2, 2} , the Range is R:{(–∞, 1)∪(2, ∞)} .

Learn more about Domain and Range here

brainly.com/question/24858133

#SPJ1

You might be interested in
Help pls and thank uu
Sergio039 [100]

Answer:

f(- 4) = - 4

Step-by-step explanation:

f(- 4) with x = - 4 gives f(- 4) = - 4

5 0
3 years ago
Solve each multi-step equation. Show your work. A - 2 + 3 = -2
Alex17521 [72]

Answer:

a is -3

Step-by-step explanation:

negative 3 minus 2 is negative 5 plus 3 is negative 2

8 0
3 years ago
HELP<br> Find the slope between the two points (6,-3) (7,2)
PtichkaEL [24]

Answer: The slope is 5

Step-by-step explanation:

8 0
2 years ago
Read 2 more answers
Pls help being timed
Katarina [22]

A. is the answer fellow user

3 0
3 years ago
Read 2 more answers
Round each mixed number to the nearest whole number and then estimate the difference. 18 9/11 - 8 3/8
mel-nik [20]

Answer:

18 9/11 rounded to the nearest whole number is 19 and 8 3/8 rounded to the nearest whole number is 8 so 19 - 8 = 11

Hope this helps :)

5 0
2 years ago
Read 2 more answers
Other questions:
  • Plz help 7th grade math ASAP
    5·2 answers
  • The airline that Vince is using has a
    11·1 answer
  • A cash register contains only five dollar and ten dollar bills. It contains twice as many five's as ten's and the total amount o
    7·1 answer
  • as a sales person at Trending Card Unlimited, Justin receives a monthly base pay plus commission on all that he sells. If he sel
    12·1 answer
  • Find the slope of the line that contains the points named.<br> A(3, 2), B(7, 8)
    5·2 answers
  • Use the box method to distribute and simplify (-5x-2)(-2x^2+6x).
    7·1 answer
  • Find the midpoint of AB for: A(7,0)|and B(0,3)​
    10·1 answer
  • HELLP!! U WILL GET I,000 POINTS Alistair writes the system of equations below. 2x+3y=−60 2x+3y=120 -----------------------------
    7·2 answers
  • PLEASE HELP I WILL MARK BRAINLIEST :))<br> Which graph has a maximum value at (1, 3)
    9·1 answer
  • Calculate the pressure if the area is<br> 10cm² and the force is 420N
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!