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3 years ago

If ƒ(x) = 2x, then ƒ -1(x) = -2x ½x x - 2

Mathematics

1 answer:

kap26 [50]3 years ago

7 0

Answer: second option

Step-by-step explanation:

To find the inverse function of the given function f(x):

$f(x)=2x$

You need to:

Substitute $f(x)=y$ into the function:

$y=2x$

Now, you need to solve for "x", to do this, you must divide both sides of the function by 2:

$\frac{y}{2}=\frac{2x}{2}\\\\\frac{y}{2}=x$

Now, replace "x" with "y" and replace "y" with "x":

$\frac{x}{2}=y$

Therefore, substituting $y=f^{-1}(x)$ you get:

$f^{-1}(x)=\frac{x}{2}$ or $f^{-1}(x)=\frac{1}{2}x$

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Point B has coordinates (1,2). The x-coordinate of point A is -8. The distance between point A and point B is 15 units. What

Xelga [282]

Answer:

The possible coordinates of point A are $A_{1} (x,y) = (-8, 14)$ and $A_{2} (x,y) = (-8, -10)$ , respectively.

Step-by-step explanation:

From Analytical Geometry, we have the Equation of the Distance of a Line Segment between two points:

$l_{AB} = \sqrt{(x_{B}-x_{A})^{2} + (y_{B}-y_{A})^{2}}$ (1)

Where:

$l_{AB}$ - Length of the line segment AB.

$x_{A}, x_{B}$ - x-coordinates of points A and B.

$y_{A}, y_{B}$ - y-coordinates of points A and B.

If we know that $l_{AB} = 15$ , $x_{A} = -8$ , $x_{B} = 1$ and $y_{B} = 2$ , then the possible coordinates of point A is:

$\sqrt{(1+8)^{2}+(2-y_{A})^{2}} = 15$

$81 + (2-y_{A})^{2} = 225$

$(2-y_{A})^{2} = 144$

$2-y_{A} = \pm 12$

There are two possible solutions:

1) $2-y_{A} = -12$

$y_{A} = 14$

2) $2 - y_{A} = 12$

$y_{A} = -10$

The possible coordinates of point A are $A_{1} (x,y) = (-8, 14)$ and $A_{2} (x,y) = (-8, -10)$ , respectively.

8 0

3 years ago

An item costs $4 before tax and $4.32 after sales tax. What is the sales tax rate?

just olya [345]

its 0.08 cents per dollar

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3 years ago

50 POINTS SHOW YOUR WORK

aliya0001 [1]

Answer:

The % growth rate is 15.8%.

Step-by-step explanation:

Let the function is given by $f(w) = a(b)^{w}$ , where f(w) is the number of a specific product produced after w weeks.

Now, given for w = 0, f(0) = 190 = a

So, the function becomes $f(w) = 190(b)^{w}$ ............. (1)

Now, it is also give that at w = 1, f(1) = 220.

So, from equation (1) we get,

$220 = 190 (b)^{1} = 190b$

⇒ b = 1.15789.

Now, b = 1 + r

⇒ 1.15789 = 1 + r

⇒ r = 0.15789

Therefore, the % growth rate is 0.15789 × 100% = 15.8% (Approx.)

8 0

3 years ago

For the graph, locate the x-intercept and y-intercept.

alexgriva [62]

X-intercept = -4
y-intercept = -8

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3 years ago

Weight is a measure of force affected by gravity. The Moon’s gravity is less than Earth’s gravity, so objects weigh less on the

Step2247 [10]

9514 1404 393

Answer:

about 1.5 pounds

Step-by-step explanation:

The moon's gravity is about 1/6 that of Earth, so a 9-lb cat would weigh about 9/6 = 1.5 pounds on the moon.

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3 years ago