All categories

2 years ago

For the function f defined by f(x)=5x−12 find f(−x),−f(x), and −f(−x).

1 answer:

3 0

$f(x) = 5x-12$

$f(-x) = 5(-x)-12 = -5x-12$

$-f(x) = -(5x-12) = -5x+12$

$-f(-x) = -(5(-x)-12) = -(-5x-12) = 5x+12$

This is probably asking you to consider the symmetry of f(x). If f(x) is equal to f(-x), then f is symmetric about the origin. If f(x) is equal to -f(x), then f is symmetric about the y-axis.

You might be interested in

Find the distance between points A(2,3) and B(5,9) round to the nearest tenth

olya-2409 [2.1K]

To calculate the distance between two points, we can use a formula that is a variation Pythagorean Theorem. Look:

$\mathsf{d=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}}$

"d" represents the distance and coordinates are expressed as follows: (x, y)

Let's go to the calculations.

$\mathsf{d=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}}\\\\ \mathsf{d=\sqrt{(5-2)^2+(9-3)^2}}\\\\ \mathsf{d=\sqrt{(3)^2+(6)^2}}\\\\ \mathsf{d=\sqrt{9+36}}\\\\ \mathsf{d=\sqrt{45}}\\\\ \mathsf{d=6.7082039324993690892275210061938...}\\\\ \underline{\mathsf{d\approxeq6.7}}$

The answer is 6.7 uc.

4 0

3 years ago

Solve for the equation, show all your work. This is an absolute value equation. You need to show both equations and the work for

VMariaS [17]

Answer:

$x=-1$ or $7$

Step-by-step explanation:

We use casework on when $3x-9=12$ and when $3x-9=-12$ .

For the first case, $3x-9=12$ , we add 9 to both sides to get

$3x=21$ .

Dividing both sides by 3 gives

$x=7.$

For the second case, $3x-9=-12$ , we add 9 to both sides to get

$3x=-3$ .

Dividing both sides by 3 gives

$x=-1$ .

Checking both cases, we plug in $x=7$ and $x=-1$ .

For the first case, we have $|3(7)-9|=|21-9|=|12|=12$ , which satisfies the equation.

For the second case, we have $|3(-1)-9|=|-3-9|=|-12|=12$ , which also satisfies the equation.

This gives us two solutions to the equation; $x=7$ and $x=-1$ .

4 0

1 year ago

Who ever can answer questions 8,9, and 10 will get 34 pts

k0ka [10]

Answer:

I am looking for this anwer to

Step-by-step explanation:

8 0

3 years ago

What multiplies to give you 15 and adds to give you -8?

Nitella [24]

Answer:

The system of equations is:

x + y = 15

xy = 15

Step-by-step explanation:

solve the first for y and substitute in the second:

y = 15-x

x(15-x) = 15

15x - x� = 15

15x - x� - 15 = 0

-x� + 15x - 15 = 0

x� - 15x + 15 = 0

7 0

2 years ago

Read 2 more answers

What's the lateral area of a right circular cone if the diameter of the base is 4 m and the slant height of the cone is 15m? Rou

Mekhanik [1.2K]

The formula for the lateral surface area of a right circular cone is:
$\pi rl$
where r is the radius of the base, and l is the slant height.
Plugging in the values we get:
$Lateral\ area= \pi \times \frac{4}{2} \times15\ m^{2}$

5 0

3 years ago