All categories

2 years ago

Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x.

1 answer:

maks197457 [2]2 years ago

5 0

F(g(x)) = [(-7x-8)/(x-1) - 8} / [(-7x - 8)/(x-1) + 7] =

[(-7x - 8 - 8(x-1)) / (x-1)] / [(-7x - 8 + 7(x-1)) / (x-1)] = (-15x) / (-15) = x.

g(f(x)) = [-7*(x-8)/(x+7) - 8] / [(x-8)/(x+7) - 1] =

[(-7x + 56 -8*(x+7)) / (x+7)] / [(x - 8 - (x + 7)) / (x+7)] = (-15x) / (-15) = x.

So since f(g(x)) = g(f(x)) = x we can conclude that f and g are inverses.

You might be interested in

Help me now !!!!!!!!!!!!!!!!

miskamm [114]

In the first diagram the value of k is 10 and in the second diagram the value of k is 15/2.

<h3>What is the triangle?</h3>

The triangle can be defined as a three-sided polygon in geometry, and it consists of three vertices and three edges. The sum of all the angles inside the triangle is 180°.

In the first diagram:

The sum of the 5k + 20 and 7k + 40 is 180

5k + 20 + 7k + 40 = 180

12k + 60 = 180

12k = 180 -60

12k = 120

k = 10

In the second diagram:

The sum of the two interior angles is equal to the exterior angle.

40 + 12k + 10 = 8k + 80

4k = 30

k = 30/4 = 15/2

Thus, in the first diagram the value of k is 10 and in the second diagram the value of k is 15/2.

Learn more about the triangle here:

brainly.com/question/25813512

#SPJ1

3 0

2 years ago

Kendra was asked to find the number of students who planned to attend the evening sympothy performance. She was told that 40 per

ch4aika [34]

Answer:

It's B

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

What set of reflections would carry hexagon ABCDEF onto itself?

Marianna [84]

When a set of reflections that carry a shape onto itself, it means that the final position of the shape will be the same as its original location

Reflections <em>(a) y=x, x-axis, y=x, y-axis </em>would carry the hexagon onto itself

First; we test the given options, until we get the true option

The rule of reflection y =x is:

$(x,y) \to (y,x)$

The rule of reflection across the x-axis is:

$(x,y) \to (x,-y)$

So, we have:

$(y,x) \to (y,-x)$

The rule of reflection y =x is:

$(x,y) \to (y,x)$

So, we have:

$(y,-x) \to (-x,y)$

Lastly, the reflection across the y-axis is:

$(x,y) \to (-x,y)$

So, we have:

$(-x,y) \to (x,y)$

So, the overall transformation is:

$(x,y) \to (x,y)$

Notice that, the original and final coordinates are the same.

This means that:

Reflections <em>(a) y=x, x-axis, y=x, y-axis </em>would carry the hexagon onto itself

Read more about reflections at:

brainly.com/question/938117

4 0

2 years ago

Pls pls pls pls pls help

raketka [301]

Answer:38x-34

Step-by-step explanation:

f(x)=x^2+3x-7

g(x)=5x-3

We multiply the entire F equation times two, (x^2+3x-7)*4=

(4x^2+12x-28)

Now the entire g equation by 2, (5x-3)*2

(10x-6)

Now we add both equation

(4x^2+12x-28)+(10x-6)

(4x^2+22x-34)

(4x*4x+22x-34)

(16x+22x-34)

38x-34

Hopefully this is correct :)))

7 0

3 years ago

What is x, if the volume of the cylinder is 768 pi cm3? Do not use units or commas in your answer.

Pachacha [2.7K]

Answer:

Step-by-step explanation:

We have that the volume of a cylinder is given by:

V = pi * (r ^ 2) * h

In this case we know the diameter, we know that the radius is half the diameter like this:

r = d / 2

r = 8/2

r = 4

Now we know that the V equals 768 pi

we replace and we have:

768 * pi = pi * (4 ^ 2) * h

768 = 16 * h

h = 768/16

h = 48

Therefore the value of x would be 48 cm

3 0

3 years ago