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
Una sucesion aumenta de 0.5 en 0.5 cuales son los primeros 6 terminos si el inicial es uno ???
Tcecarenko [31]
1, 1.5, 2, 2.5, 3, 3.5

Y si no se cuenta el uno:

1.5, 2, 2.5, 3, 3.5, 4.
6 0
3 years ago
If a 90°degree angle is bisected, the two angles created by the bisector will equal?
katen-ka-za [31]

Answer:

45 degrees

Step-by-step explanation:

when an angle is bisected both angles formed are equal, so 90/2=45

5 0
3 years ago
Read 2 more answers
Can someone please help me the questions are in the picture
skelet666 [1.2K]
B
C
..................
3 0
3 years ago
Match the inequality to the graph of its solution.
MrRissso [65]
A. c <= -4 so is the top graph;
b. c > 4 so is the second graph;
c. c < 10 so will be a graph with an open circle starting at 10 and going left towards negative infinity
3 0
3 years ago
please help me ASAPif asked is this a text or a quiz- this is a practiceif asked if a agree to the terms and guidelines- I agree
STatiana [176]

We notice that the common ratio of teh sequence is 10, and that the first term is -0.56, then the recursive formula is:

a_{n+1}=a_n\cdot10,a_1=-0.56

3 0
1 year ago
Other questions:
  • Ari bought a DVD that originally cost $15 on sale for 20% off. The sales tax is 5%. How much did Ari pay for the DVD, including
    6·1 answer
  • Find the value of each variable and the measure of each angle​
    10·1 answer
  • a materials scientist has 56 pounds of a liquid. she uses most of the liquid to fill 7 beakers. The remaining liquid fill 1/9 of
    15·1 answer
  • An lpn earned a gross pay of 650.04 last week. if 21 1/2% of her gross paycheck is taken out in taxes, what is her bring home pa
    9·2 answers
  • If 3/x=5/y, what is the value of y/x?
    11·2 answers
  • SOLVE FOR X SHOW YOUR WORK 27+6x=99 X=?
    8·2 answers
  • The density of a block of cheese is 8 g/cm3. If the mass of the block is 260 g, the width of
    9·1 answer
  • Nick, Sarah and Gavyn share some sweets in the ratio 2:3:3. Nick gets 28 sweets. How many did Gavyn get?
    8·1 answer
  • Geometry triangle help pls
    12·1 answer
  • Please help me with this question!
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!