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Julli [10]
3 years ago
13

For all values of x, f(x) = 2x-3 and g(x) = x^2 + 1 a) Find fg(x) Simplify and give your answer in the form ax^2 + b b) Find gf(

x).
Mathematics
1 answer:
Inessa [10]3 years ago
6 0

Answer:

fg(x) = 2x² - 1

gf(x) = 4x²-12x +10

Step-by-step explanation:

Given the functions f(x) = 2x-3 and g(x) = x^2 + 1

a) f(g(x)) = f(x²+1)

f(x²+1) = 2(x²+1) -3

f(x²+1)= 2x²+2 -3

f(x²+1) = 2x² - 1

fg(x) = 2x² - 1

Hence function fg(x) is 2x² - 1

b) gf(x) = g(2x-3)

g(2x-3) = (2x-3)² + 1

g(2x-3) = (2x-3)(2x-3) + 1

g(2x-3) = 4x²-6x-6x+9 + 1

g(2x-3) = 4x²-12x +10

gf(x) = 4x²-12x +10

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Answer:

Essentially, slope is rise/run. Rise is how many units up the graph, and run is how far to the left or right it goes. Rise will be negative if it's going down, and run will be negative if it's going left. There's two ways to find the slope in this case.

1. Stick to the more visual aspect of it, and count how many units up from one point to the next point. Point (1,2) is 2 units up from point (0,0). Then you count how many units right or left it goes. In this case, it's 1 towards the right. This means the rise/run comes out to be 2/1, which means the slope=2.

2. Look at the equations. y=mx+b is the linear format for these lines. y is the y coordinate, m is the slope, x is the x coordinate, and b is the y intercept (the point where x=0). These two lines have shared slope values, which means the slope for both of them is 2.

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3 0
3 years ago
The length of the hypotenuse of a 30 - 60 - 90 triangle is 16 cm.
xeze [42]

Answer:

8, 8x square root of 3

Step-by-step explanation:

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3 years ago
Write the addition sentence below as a multiplication sentence.<br> 2 + 2 + 2 + 2 + 2 + 2 = 12
Nastasia [14]

Answer:

6*2 = 12

Step-by-step explanation:

2 + 2 + 2 + 2 + 2 + 2 = 12

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5 0
3 years ago
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Valentin [98]
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7 0
2 years ago
Two consecutive odd integers are such that one-third the smaller is greater than one-seventh of the larger one by 6. Find the nu
vaieri [72.5K]

Answer:

the number is 33 and 35 respectively

Step-by-step explanation:

The computation is shown below:

Let us assume X and X + 2 are the two consecutive odd integers

Now the equation is

(X ÷ 3) = ((X + 2) ÷ 7) + 6

(X ÷ 3) = (X + 2 + 6 × 7) ÷ 7

(X ÷ 3) = (X + 2 + 42) ÷ 7

(X ÷ 3) =  (X + 44) ÷ 7

Now do the cross multiplication

7X  = 3(X + 44)

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X = 33

And, X + 2 = 33 + 2 = 35

hence, the number is 33 and 35 respectively

5 0
3 years ago
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