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HACTEHA [7]
3 years ago
6

Use the functions f(x)=2x and g(x)= x^2+1 to find the value of each expression.

Mathematics
1 answer:
musickatia [10]3 years ago
8 0

Answer:

First, you learned (back in grammar school) that you can add, subtract, multiply, and divide numbers. Then you learned that you can add, subtract, multiply, and divide polynomials. Now you will learn that you can also add, subtract, multiply, and divide functions. Performing these operations on functions is no more complicated than the notation itself. For instance, when they give you the formulas for two functions and tell you to find the sum, all they're telling you to do is add the two formulas. There's nothing more to this topic than that, other than perhaps some simplification of the expressions involved.

Step-by-step explanation:

To find the answers, all I have to do is apply the operations (plus, minus, times, and divide) that they tell me to, in the order that they tell me to.

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

= [3x + 2] + [4 – 5x]

= 3x + 2 + 4 – 5x

= 3x – 5x + 2 + 4

= –2x + 6

(f – g)(x) = f (x) – g(x)

= [3x + 2] – [4 – 5x]

= 3x + 2 – 4 + 5x

= 3x + 5x + 2 – 4

= 8x – 2

(f  × g)(x) = [f (x)][g(x)]

= (3x + 2)(4 – 5x)

= 12x + 8 – 15x2 – 10x

= –15x2 + 2x + 8

\left(\small{\dfrac{f}{g}}\right)(x) = \small{\dfrac{f(x)}{g(x)}}(  

g

f

​  

)(x)=  

g(x)

f(x)

​  

 

= \small{\dfrac{3x+2}{4-5x}}=  

4−5x

3x+2

​  

 

My answer is the neat listing of each of my results, clearly labelled as to which is which.

( f + g ) (x) = –2x + 6

( f – g ) (x) = 8x – 2

( f  × g ) (x) = –15x2 + 2x + 8

\mathbf{\color{purple}{ \left(\small{\dfrac{\mathit{f}}{\mathit{g}}}\right)(\mathit{x}) = \small{\dfrac{3\mathit{x} + 2}{4 - 5\mathit{x}}} }}(  

g

f

​  

)(x)=  

4−5x

3x+2

​

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the outside fence has a 64 feet perimeter

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A new motorcycle has a value of $8000 every year is value decreased by $500 which function can be used to find why the value of
vredina [299]
F(x) = 500x-8000

500 times the number of years (x), subtracted by the original price (8000)
5 0
3 years ago
Simplify.<br><br> 15 20 24+20
WINSTONCH [101]

Answer:

-5 divide by 28

Step-by-step explanation:

so the question supposed be " 15-20 divided by 2(4) + 20

15-20 which is also 15 + (-20)= -5

2(4)=8, 8+20=28

so it can simplify into -5 / 28

(hope it helps :)

5 0
2 years ago
Find how many six-digit numbers can be formed from the digits 2, 3, 4, 5, 6 and 7 (with repetitions), if:
Goshia [24]

Answer:

case 1 = 2592

case 2 =  729

case 1 + case 2 =  2916

(this is not a direct adition, because case 1 and case 2 have some shared elements)

Step-by-step explanation:

Case 1)

6 digits numbers that can be divided by 25.

For the first four positions, we can use any of the 6 given numbers.

For the last two positions, we have that the only numbers that can be divided by 25 are numbers that end in 25, 50, 75 or 100.

The only two that we can create with the numbers given are 25 and 75.

So for the fifth position we have 2 options, 2 or 7,

and for the last position we have only one option, 5.

Then the total number of combinations is:

C = 6*6*6*6*2*1 = 2592

case 2)

The even numbers are 2,4 and 6

the odd numbers are 3, 5 and 7.

For the even positions we can only use odd numbers, we have 3 even positions and 3 odd numbers, so the combinations are:

3*3*3

For the odd positions we can only use even numbers, we have 3 even numbers, so the number of combinations is:

3*3*3

we can put those two togheter and get that the total number of combinations is:

C = 3*3*3*3*3*3 = 3^6 = 729

If we want to calculate the combinations togheter, we need to discard the cases where we use 2 in the fourth position and 5 in the sixt position (because those numbers are already counted in case 1) so we have 2 numbers for the fifth position and 2 numbers for the sixt position

Then the number of combinations is

C = 3*3*3*3*2*2 = 324

Case 1 + case 2 = 324 + 2592 = 2916

4 0
3 years ago
C=2(y-k) solve for y​
marshall27 [118]

Answer:

\blue{y = \dfrac{C + 2k}{2}}

Step-by-step explanation:

C = 2(y - k)

C = 2y - 2k

C + 2k = 2y

\dfrac{C + 2k}{2} = y

y = \dfrac{C + 2k}{2}

5 0
2 years ago
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