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guajiro [1.7K]
3 years ago
9

Determine whether the statements are True or False. Justify your answer with an explanation.

Mathematics
1 answer:
frez [133]3 years ago
7 0

Problem 1

<h3>Answer: False</h3>

---------------------------------

Explanation:

The notation (f o g)(x) means f( g(x) ). Here g(x) is the inner function.

So,

f(x) = x+1

f( g(x) ) = g(x) + 1 .... replace every x with g(x)

f( g(x) ) = 6x+1 ... plug in g(x) = 6x

(f o g)(x) = 6x+1

Now let's flip things around

g(x) = 6x

g( f(x) ) = 6*( f(x) ) .... replace every x with f(x)

g( f(x) ) = 6(x+1) .... plug in f(x) = x+1

g( f(x) ) = 6x+6

(g o f)(x) = 6x+6

This shows that (f o g)(x) = (g o f)(x)  is a false equation for the given f(x) and g(x) functions.

===============================================

Problem 2

<h3>Answer: True</h3>

---------------------------------

Explanation:

Let's say that g(x) produced a number that wasn't in the domain of f(x). This would mean that f( g(x) ) would be undefined.

For example, let

f(x) = 1/(x+2)

g(x) = -2

The g(x) function will always produce the output -2 regardless of what the input x is. Feeding that -2 output into f(x) leads to 1/(x+2) = 1/(-2+2) = 1/0 which is undefined.

So it's important that the outputs of g(x) line up with the domain of f(x). Outputs of g(x) must be valid inputs of f(x).

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Solve this system of equations using substitution. Put your answer in ordered pair form, (x,y).
Gelneren [198K]
2x + 5y = 2
-3x - y =-3

-3x - y = -3
y = 3x - 3

substitute y = 3x - 3 into the first equation.

2x + 5y = 2
2x + 5(3x - 3) = 2
2x + 15x - 15 = 2
17x - 15 = 2

solve for x in 17x - 15 = 2

17x - 15 = 2
17x = 2 + 15
17x = 17
x = 1

substitute x = 1 into y = 3x - 3

y = 3x - 3
y = 3(1) - 3
y = 3 - 3
y = 0

(1, 0) << the answer

hope this helped, God bless!
8 0
3 years ago
A kite is flying 20 ft off the ground. Its line is pulled taut and casts a 15 ft - shadow. Find the length of the line. If neces
Kryger [21]

Answer:

The answer to your question is 25 ft

Step-by-step explanation:

Data

height = 20 ft

leg = 15 ft

length of the line = ?

To solve this problem use the Pythagorean theorem.

Height = short leg = b

leg = long leg = a

length of the line = hypotenuse = c

- Substitution

         c² = (20)² + (15)²

-Simplification

         c² = 400 + 225

         c² = 625

-Result

         c = \sqrt{625}

         c = 25 ft

6 0
3 years ago
Solve the system of equations using substitution. y = x + 6 y = –2x – 3 (4, –11) (1, 7) (–3, 3)
sergejj [24]
The answer to the question

5 0
3 years ago
Which equation represents a line that passes through (2, –0.5) and has a slope of 3?
Kitty [74]
A slope of 3 means the gradient is 3 so we get y=3x+c as derived from the linear formula. we then sub in x=2 and y=-0.5. this gives us c=-6.5.

The equation would be y=3x-6.5

I think this is right.
4 0
3 years ago
Read 2 more answers
If g(x) = 2x + 1 and fog (x)=6x-2, find f(x).​
Nostrana [21]

Answer:

g(x) = f(x) \\ 2x + 1 = 6x - 2 \\ 2x - 6x =  - 2 - 1 \\  - 4x =  - 3 \\ x =  \frac{3}{4}

6 0
2 years ago
Read 2 more answers
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