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3 years ago

Use f(x) = 1 2 x and f -1(x) = 2x to solve the problems.

Mathematics

1 answer:

AVprozaik [17]3 years ago

4 0

Answer:

The answer to your question is below

Step-by-step explanation:

Functions

f(x) = 12x f⁻¹(x) = 2x

a) f⁻¹(-2) = 2(-2)

f⁻¹(-2) = -4

b) f(-4) = 12x

f(-4) = 12(-4)

f(-4) = -48

c) f(f⁻¹(-2)) =

f(f⁻¹(x)) = 12(2x) = 24x

f(f⁻¹(-2)) = 24(-2) = -48

I think your functions are wrong they must be f(x) = 1/2x f⁻¹(x) = 2x

a) f⁻¹(-2) = 2(-2)

= -4

b) f(-4) = 1/2(-4)

= -2

c) f(f⁻¹(x)) = 1/2(2x)

= x

f(f⁻¹(-2)) = -2

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Montano1993 [528]

Answer:

I think 25.50

Step-by-step explanation:

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3 years ago

Suppose that a cyclist began a 476

mojhsa [17]

Well, we know the cyclist left the western part going eastwards, at the same time the car left the eastern part going westwards

the distance between them is 476 miles, and they met 8.5hrs later

let's say after 8.5hrs, the cyclist has travelled "d" miles, whilst the car has travelled the slack, or 476-d, in the same 8.5hrs

we know the rate of the car is faster... so if the cyclist rate is say "r", then the car's rate is r+33.2

thus $\bf \begin{array}{lccclll}
&distance&rate&time\\
&-----&-----&-----\\
\textit{eastbound cyclist}&d&r&8.5\\
\textit{westbound car}&476-d&r+33.2&8.5
\end{array}\\\\
-----------------------------\\\\
\begin{cases}
\boxed{d}=8.5r\\\\
476-d=(r+33.2)8.5\\
----------\\
476-\boxed{8.5r}=(r+33.2)8.5
\end{cases}$

solve for "r", to see how fast the cyclist was going

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3 years ago

Josh had 4/5 of a liter of soda to share with two of his friends. If he pours an equal amount of soda in 3 cups how much will ea

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3 years ago

The Oxy coordinate plane for two parallel lines a and a' has the equations 2x - 3y-1 = 0 and 2x - 3y + 5 = 0. respectively. Whic

Andru [333]

Answer:

Remember that a vector translation can be written as:

T(a, b)

And if we apply this to a random point, (x, y), the translation gives:

T(a, b)(x, y) = (x + a, y + b)

now, remember that a general line can be written as:

y = m*x + s

Then a point of that line can be written as: (x, m*x + s)

Then if we apply the translation to a point in the line, we get:

T(a, b)(x, m*x + s) = (x + a, m*x + s + b)

Here we have two lines:

2x - 3y - 1 = 0

2x - 3y + 5 = 0

First, let's rewrite both of these in the slope-intercept form:

y = (2/3)*x - 1/3

y = (2/3)*x + 5/3

Now let's assume that we apply a translation to the first line, that has points of the form (x, (2/3)*x - 1/3), such that we want to get points of the form:

(x, (2/3)*x + 5/3).

Then we must have:

T(a, b)(x, (2/3)*x - 1/3) = (x + a, (2/3)*x - 1/3 + b) = (x, (2/3)*x + 5/3).

Then we need to solve:

(x + a, (2/3)*x - 1/3 + b) = (x, (2/3)*x + 5/3).

This means that:

x + a = x

(2/3)*x - 1/3 + b = (2/3)*x + 5/3

From the first equation, we can see that a = 0

Now we can solve the second one to find the value of b.

(2/3)*x - 1/3 + b = (2/3)*x + 5/3

subtracting (2/3)*x in both sides, we get:

-1/3 + b = 5/3

b = 5/3 + 1/3

b = 6/3 = 2

b = 2

Then the vector translation is:

T(0, 2)

So it moves the whole line 2 units upwards.

7 0

3 years ago

Norman buys two cakes. One cake cost 40 cents and the other costs a quarter. How much does he spend in total?

Ivan

Answer: 50 cents

Step-by-step explanation:

Norman buys two cakes. One cake cost 40 cents and the other costs a quarter. Based on this, the cost of the second cake will be:

= 1/4 × 40

= 10 cent

Now, the total amount spent in total will be:

= 40 cents + 10 cents

= 50 cents

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3 years ago