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
Nina [5.8K]
2 years ago
9

For f(x) = 9x and g(x) = x + 3, find the following functions.

Mathematics
1 answer:
NeX [460]2 years ago
7 0

Answer:

a)  9*x + 27

b) 9*x+3

c) 45

d) 21

Step-by-step explanation:

since (f o g)(x) = f (g(x))  , then

a) (f o g)(x) = f (x + 3) = 9*(x+3) = 9*x + 27

similarly

b) (g o f)(x) = g (f(x)) = g ( 9x) = (9*x)+3 = 9*x+3

c) for x=2

(f o g)(2) = 9*2 + 27 = 45

d) for x=2

(g o f )(2) =  9*2 +3 = 21

thus we can see that the composition of functions is not necessarily commutative  

You might be interested in
What is the mapping notation that will transform triangle ABC to triangle A'B'C'?
MissTica

Answer:

I cant see it so can u do something so i can see it plz

6 0
2 years ago
The symbol ⊕ is used to denote exclusive or, so p ⊕ q ≡ (p v q) ^ ~ (p ^ q).
Elan Coil [88]

I'll use text forms of the logical symbols because copying/pasting on mobile is annoying.

⊕ = XOR

∨ = OR

∧ = AND

~ = NOT

↔ = IFF (meaning "if and only if")

→ = IMP (short for "implies")

and for logical equivalence I'll use a regular equal sign.

Then

p XOR q = (p OR q) AND NOT (p AND q)

(a) By definition of XOR, we have

p XOR p = (p OR p) AND NOT (p AND p)

= p AND NOT p

and this is tautologically FALSE.

(b) To rewrite XOR, first distribute the NOT over the AND using DeMorgan's law:

NOT (p AND q) = NOT p OR NOT q

Then we can interchange the AND and ORs using their respective distributive properties. That is,

p XOR q = (p OR q) AND (NOT p OR NOT q)

= (p AND (NOT p OR NOT q)) OR (q AND (NOT p OR NOT q))

= ((p AND NOT p) OR (p AND NOT q)) OR ((q AND NOT p) OR (q AND NOT q))

Both (p AND NOT p) and (q AND NOT q) are tautologically FALSE, so the truth value of either OR depends only on the other statements, so we have

p XOR q = (p AND NOT q) OR (q AND NOT p)

Recall the definition of IFF:

p IFF q = (p IMP q) AND (q IMP p)

Also recall that IMP is logically equivalent to

p IMP q = p OR NOT q

Then we have

p IFF q = (p OR NOT q) AND (q OR NOT p)

so that its negation is

NOT (p IFF q) = NOT ((p OR NOT q) AND (q OR NOT p))

= NOT (p OR NOT q) OR NOT (q OR NOT p)

= (NOT p AND q) OR (NOT q AND p)

The statements in bold match, so p XOR q is indeed equivalent to NOT (p IFF q).

3 0
2 years ago
Mrs. Cisneros earns $300 per week if she works exactly 40 hours. She earns $12 for each additional hour beyond 40 hours. Which i
lys-0071 [83]

Answer:

300+ 12h=450

12h=150

h=12.5

Step-by-step explanation:

7 0
2 years ago
Andrea needs 4 kilograms of oranges. The scale below shows the weight of the oranges she has in her kitchen. Part A. About how m
juin [17]
We know that

<span>each space on the balance represents
1 kg/ 10 spaces----------> 0.10 kg
in the picture there are 14 spaces
so
14*0.1-------> 1.4 Kg
</span>
Part A) About how many kilograms of oranges does Andrea have? Round your answer to the nearest kilogram

Andrea has 1.4 kg of oranges------> to the nearest kilogram-----> 1 Kg

the answer is
1 kg

Part B) About how many more kilograms of oranges does Andrea need?
Andrea needs=(4 Kg-1.4 Kg)------> 2.6 Kg

the answer part B) is
2.6 Kg
8 0
3 years ago
PLEASE HELP ME, and explain it please please please &lt;3
ser-zykov [4K]
The answer would be f(x)= x+47
7 0
2 years ago
Other questions:
  • The volume of a sphere is found using the formula . If the volume of a sphere is 36 , what is the radius, in feet?
    12·1 answer
  • Use the order of operations to simplify the following expression
    12·1 answer
  • Can someone help me?
    10·1 answer
  • Solve the compound inequality. -2x&lt;2x-4&lt;4
    13·2 answers
  • Please someone solve this
    11·1 answer
  • ^^^<br> Quickly answer please
    8·2 answers
  • Whats 2x2x2x2x2x2x2x2x2x2x2x2x2
    13·1 answer
  • Find the value of x in the triangle shown below.
    15·1 answer
  • Use graphing technology to find the range of the function f(x)=1/2x+2​
    15·1 answer
  • Eight times the quotient of x and 2
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!