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2 years ago

Identify the inverse g(x) of the given relation f(x).f(x) = {(8, 3), (4, 1), (0, –1), (–4, –3)}

Mathematics

2 answers:

laiz [17]2 years ago

5 0

F(x) = {(8, 3), (4, 1), (0, -1), (-4, -3)}
f(x) = ¹/₂x - 1

f(x) = ¹/₂x - 1
  y = ¹/₂x - 1
  x = ¹/₂y - 1
+ 1 + 1
  x + 1 = ¹/₂y
  2(x + 1) = 2(¹/₂y)
2(x) + 2(1) = y
2x + 2 = y
2x + 2 = f⁻¹(x)
2x + 2 = g(x)

g(x) = {(3, 8), (1, 4), (-1, 0), (-3, -4)}
g(x) = 2x + 2

Over [174]2 years ago

3 0

correct answer is g(x) = {(3, 8), (1, 4), (-1, 0), (-3, -4)}

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How is (s-t)(s/t) equivalent to (s^2/t) -s

tigry1 [53]

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2 years ago

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If 1 British pound equals 1.6972 Swiss francs, then 1 Swiss franc equals approximately how many British pounds?

marusya05 [52]

Start with "<span>1 British pound equals 1.6972 Swiss francs" and make a conversion factor out of it:
</span>
1.6972 Sw. F.
------------------
1 Br. pound

Invert this, obtaining:

1 Br. pound
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1.6972 Sw. F.

Here's where the fun begins. To find the value of 1 SFr in BPS, mult.

1 SFr by the above conversion factor:

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This is a formal way in which to do this problem. You could obtain the same result if you'd simply invert

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1.6972 Sw. F.

and divide 1 by 1.6972.

8 0

2 years ago

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Maisie has saved up $50 to buy concert tickets, but the tickets cost $125. She is able to earn $15 per day by walking her neighb

Greeley [361]

Answer:

15d + 50 = 125

15d = 75

5 days

Step-by-step explanation:

Her total must equal $125.

She has $50 so far.

50 + _____ = 125

In the blank, we will put what she will earn by walking the dogs.

Each day she will earn $15. In d number of days, she will earn 15d.

The equation is:

50 + 15d = 125

15d + 50 = 125

We can subtract 50 from both sides to get

15d = 75

Now we solve the equation to find the number of days.

We divide both sides by 15.

15d/15 = 75/15

d = 5

She will need to walk the dogs for 5 days.

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2 years ago

What are the factors of the polynomial function? Use the rational root theorem to determine the factors. f(x) = 2x³ + x² - 8x -

fredd [130]

Answer:

( x + 2 ) ( x - 2 ) ( 2x + 1)

Step-by-step explanation:

coefficient of x³ is 2 and denote it with q and denote -4 as p

the set of possible rational roots through rational theorem will be within ± (p/q)

now factors of -4 are ±(1,2,4) and factors of 2 are ± (1,2) the possible rational roots are ± ( 1/1, 1/2, 2/1, 2/2, 4/1, 4/2) which reduces to ± (1, 1/2, 2, 4)

substitute each of the value into the equation

f(x) = 2x³ + x² - 8x - 4 to the root ( that gives f(x) = 0)

the equation can be made easy writing it in reduced form

2x³ + x² - 8x - 4

(2x³ + x²) - (8x + 4)

x² (2x + 1) - 4 (2x + 1)

(x² - 4) (2x + 1)

( x + 2 ) ( x - 2) ( 2x + 1) are the factors which correspond to 2, -2, -1/2 roots

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2 years ago

Find a matrix representation of the transformation L(x, y) = (3x + 4y, x − 2y).

mario62 [17]

Answer:

$\left[\begin{array}{cc}x&y\end{array}\right] * \left[\begin{array}{cc}3&1\\4&-2\end{array}\right] = \left[\begin{array}{cc}3x+4y&x-2y\end{array}\right]$

Step-by-step explanation:

The general matrix representation for this transformation would be:

$\left[\begin{array}{cc}x&y\end{array}\right] * A = \left[\begin{array}{cc}3x+4y&x-2y\end{array}\right]$

As the matrix A should have the same amount of rows as columns in the firs matrix and the same amount of columns as the result matrix it should be a 2x2 matrix.

$\left[\begin{array}{cc}x&y\end{array}\right] * \left[\begin{array}{cc}a&b\\c&d\end{array}\right] = \left[\begin{array}{cc}3x+4y&x-2y\end{array}\right]$

Solving the matrix product you have that the members of the result matrix are:

3x+4y = a*x + c*y

x - 2y = b*x + d*y

So the matrix A should be:

$\left[\begin{array}{cc}3&1\\4&-2\end{array}\right]$

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2 years ago