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
Basile [38]
3 years ago
11

For the given function f and g, complete parts (a)-(h). For parts (a)-(d), also find the domain.

Mathematics
1 answer:
kakasveta [241]3 years ago
5 0

Answer:

a) (f + g)(x) = 9x + 1

Domain: x ε R

b) (f - g)(x) = (-5x + 13)

Domain: x ε R

c) (f.g)(x) = 14x² + 37x - 42

Domain: x ε R

d) (f/g)(x) = (2x + 7)/(7x -6)

Domain: (x ε R except x = 6/7)

e) (f + g)(7) = 64

f) (f - g)(2) = 3

g) (f.g)(3) = 195

h) (f/g)(x) = 1/3

Step-by-step explanation:

f(x) = 2x + 7, g(x) = 7x - 6

a) (f + g)(x) = f(x) + g(x) = (2x + 7) + (7x - 6)

(f + g)(x) = 9x + 1

Since x is defined for functions f & g for all real numbers, the domain of (f + g)(x) is x ε R

b) (f - g)(x) = f(x) - g(x) = (2x + 7) - (7x - 6)

(f - g)(x) = (-5x + 13)

Since x is defined for functions f & g for all real numbers, the domain of (f - g)(x) is x ε R

c) (f.g)(x) = f(x) × g(x) = (2x + 7)(7x - 6)

(f.g)(x) = 14x² - 12x + 49x - 42 = 14x² + 37x - 42

Since x is defined for functions f & g for all real numbers, the domain of (f.g)(x) is x ε R

d) (f/g)(x) = f(x)/g(x) = (2x + 7)/(7x -6)

x is defined for functions f & g for all real numbers, the domain of (f/g)(x) will be x ε R except when the denominator vanishes (that is, goes to zero). This will cause the function to take up values of ∞.

This will happen when 7x - 6 = 0, x = 6/7.

Therefore, the domain of (f/g)(x) is x ε R except the point, x = 6/7.

e) (f + g)(7) = 9(7) + 1 = 64

f) (f - g)(2) = -5(2) + 13 = 3

g) (f.g)(3) = 14(3²) + 37(3) - 42 = 195

h) (f/g)(27) = (2(27) + 7)/(7(27) - 6) = 61/183 = 1/3

Hope this Helps!!!

You might be interested in
Compare 10x(8+2) and 20x(8+2)
Artist 52 [7]

the 20x(8+2) is just two times greater as its 200 instead of 100 which is the other answer

4 0
3 years ago
I barely ask questions but I really need help with #3 and a little with 4. On number four I got 1 1/20 which doesn’t seem right.
uranmaximum [27]
Let r, g and b represent red, green and blue.

r+g+b = 74

r=g-1

b=r+g

Again, r+g+b = 74.  Let's substitutte r+g for b:  r+g+(r+g) = 74.

Next, let's eliminate r.  Use r=g-1.  Then      g-1  + g + g-1 + g = 74

Combining the g terms,  4g - 2 = 74     => 4g = 76   =>  g = 19

Recall that r=g-1
and 
b=r+g

Find r.  If r=g-1, and g=19, then r = 19-1=18

Find b:  b = r+g = 18+19=37

So there are 37 blue candies, 18 red candies and 19 green candies.

Check:  37+18+19=74 ???  Yes.
8 0
3 years ago
You are taking a​ multiple-choice test that has 55 questions. each of the questions has 33 answer​ choices, with one correct ans
siniylev [52]
<span>Each question has 5 possible choices for an answer>
1st question: 5 ways
2nd question: 5 ways
.......
12th question: 5 ways

----
Total # of possible answers 5*5*5...*5*5 = 5^12 = 244,140,625
-----
Cheers,
Stan H.
========================= 
The answer is 244,140,625</span>
5 0
3 years ago
80 members decreased by 65%
prisoha [69]
There are now 28 members
all you do is 80 times 0.65 = 52
but you still have to subtract 80 - 52 to find the number of members left 
SOOOO
28 members still there 
52 members quit
7 0
3 years ago
Read 2 more answers
Write two expressions that could be used to find 105% of x. ANSWER TODAY!! :) thanks
Margaret [11]

First way: x * 1.05

This computes directly what 105% of x will be.


Second way: x + (x * 0.05)

This takes x (which is 100%) and adds 5% of x to it.

6 0
3 years ago
Read 2 more answers
Other questions:
  • Please Help, Due Soon<br><br><br>What is −1/2 − (−4/5)<br><br><br>= x
    14·1 answer
  • 1 Find the value of x in the triangle shown below.​
    7·1 answer
  • What additional information would you need to prove that ΔABC ≅ ΔDEF by SSS?
    10·2 answers
  • What is 100% of 94 in a decimal
    9·1 answer
  • Evaluate 5-4÷(6-(3-1))
    5·1 answer
  • Nelson decides to invest $1,000,000 in a period annuity that
    12·1 answer
  • It takes Maya 30 minutes to solve 5 logic puzzles and it takes Amy 28 minutes to solve 4 logic puzzles use models to show the ra
    12·1 answer
  • Which is bigger 2/5 or 3/10
    5·2 answers
  • Can you answer this pls​
    7·1 answer
  • Use the discriminant to determine how many and what kind of solutions the quadratic equation 3x^2 + 4x = - 5 has.
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!