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]
2 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]2 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
There are three executives in an office, ages 56, 57, and 58. If a 57-year-old executive enters the room, the
vova2212 [387]

Answer:

option (c) The mean age will stay the same but the variance will decrease

Step-by-step explanation:

Case I: For 3 executives of ages 56, 57 and 58

Number of executives, n = 3

Mean = \frac{\textup{56 + 57 + 58 }}{\textup{3}}

or

Mean = 57

Variance = \frac{\sum{(Data - Mean)^2}}{\textup{n-1}}

or

Variance = \frac{(56 - 57)^2+(57-57)^2+(58-57)^2}{\textup{3-1}}

or

Variance = \frac{1+0+1}{\textup{2}}

or

Variance = 1

For Case II: For 4 executives of ages 56, 57, 58 and 57

Number of executives, n = 4

Mean = \frac{\textup{56 + 57 + 58 + 57 }}{\textup{4}}

or

Mean = 57

Variance = \frac{\sum{(Data - Mean)^2}}{\textup{n-1}}

or

Variance = \frac{(56 - 57)^2+(57-57)^2+(58-57)^2+(57-57)^2}{\textup{4-1}}

or

Variance = \frac{1+0+1+0}{\textup{3}}

or

Variance = 0.67

Hence,

Mean will remain the same and the variance will decrease

Hence,

The correct answer is option (c) The mean age will stay the same but the variance will decrease

3 0
3 years ago
The parent function f(x) = x3 is translated to form g(x), as shown on the graph. The translated function can be written in the f
OLEGan [10]

Answer: First option

Step-by-step explanation:

By definition, the horizontal shift depends on the value of <em>h </em>and the vertical shift depends on the value of <em>k</em><u>.</u>

f(x)=(x-h)^3 indicates that the function if shifted to the right <em>h </em> units.

f(x)=(x+h)^3 indicates that the  function if shifted to the left <em>h </em> units.

f(x)=f(x)-k indicates that the  function if shifted  down <em>k </em> units.

f(x)=f(x)+k indicates that the  function if shifted up <em>k </em> units.

Then:

If <em>h </em>is positive, the graph will shift to the right.

If <em>k </em>is negative, the graph will shift down.

 As you can see in the graph, the function is shifted 4 units to the right and 2 units down. Therefore g(x) has the form:

 g(x)=(x-4)^3-2

Where:

h=4\\k=-2

7 0
2 years ago
I need help on this ​
spin [16.1K]

Answer:

point a is (-1,-2)

point b is (-2,-4)

point c is (-3,-4)

point d is (-4-2)

3 0
2 years ago
Square root of 80 to the power of 2
Alex Ar [27]
80 would be your answer for this question
3 0
2 years ago
Read 2 more answers
Consider the following polynomial.
vfiekz [6]

Answer:

The equivalent factored form of this equation is (x² + 49)(x - 6)

Step-by-step explanation:

<em>x³ - 6x² + 49x - 294</em>

First, group the first and second terms together and group the last two terms together.

<em>(x³ - 6x²) + (49x - 294)</em>

Find the greatest common factor of both parentheses and factor them.  

x²(x - 6) + 49(x - 6)

Now, since the two terms in the parentheses are the same, then we have factored the equation correctly.

So, the factored form of the equation is (x² + 49)(x - 6)

3 0
2 years ago
Read 2 more answers
Other questions:
  • The value of y is inversely proportional to the value of x. When y=40, x=5. What is the value of y when x=8
    6·1 answer
  • Sean is helping his dad build a tiled walkway in their backyard. The walkway will be 60 feet long and 2 feet wide. The local har
    7·1 answer
  • 116.15 round to nearest 10th
    12·1 answer
  • When temperature is zero degree Celsius, the Fahrenheit temperature is 32. When the Celsius temperature is 100, the correspondin
    11·1 answer
  • What is the slope of the line in the equation below?<br><br> y = 3x + 2
    13·2 answers
  • The hand on a clock shows 6:00pm what is the measure of the angle
    8·2 answers
  • A cone of base 10 cm^2 and a height of 60 cm has what volume?
    6·1 answer
  • The solution of a system of linear equations is where the two lines intersect....
    8·2 answers
  • Need help with this
    10·1 answer
  • What is the distance between A(5, 4) and<br> B(2, -3)?
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!