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3 years ago

Write the equation for the inverse of the function. y = sin x

Mathematics

2 answers:

MakcuM [25]3 years ago

7 0

Answer:

The answer is $\sin^{-1}$ x = y

Step-by-step explanation:

We need to find the inverse of the function

y = sinx

Taking $\sin^{-1}$ on both sides

$\sin^{-1}$ y = $\sin^{-1}$ sinx

$\sin^{-1}$ y = x

Substituting x to y and y to x

$\sin^{-1}$ x = y

This is the required inverse of the function

The graph of the function and its inverse is symmetric about y = x

The answer is $\sin^{-1}$ x = y

NemiM [27]3 years ago

6 0

Answer:

y = Arcsin x

Step-by-step explanation:

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3 years ago

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3 years ago

At midnight, the temperature was 34°F. By 6:00 a.m. it had dropped 8°, and by noon it had increased by 11°. What was the tempera

olga_2 [115]

Answer:

The temperature at noon was 37 °F.

Step-by-step explanation:

Given:

Temperature at midnight is 34 °F.

Reduction in temperature by 6:00 a.m. is 8°. So, temperature after reduction is given as the difference in temperature at midnight and morning.

Therefore, temperature by 6:00 a.m. in the morning is given as:

Reduced temperature = Midnight temperature - Reduction in temperature.

Reduced temperature = 34 °F - 8 °F = 26 °F.

Now, by noon, the temperature is increased by 11 °F. Therefore, the final temperature by noon is addition of 11 degree to the temperature that was in the morning. Therefore,

Temperature at noon = Temperature in morning + Increase in temperature.

Temperature at noon = 26 °F + 11 °F = 37 °F.

So, the temperature at noon is a 3 °F increase to the temperature at midnight and is equal to 37 °F.

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3 years ago

5/8 is a fraction which represents a bit over half of a number

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3 years ago

Determine the Vertex of the following absolute value function.

prisoha [69]

Answer:

vertex = (-4, 5)

Step-by-step explanation:

In general, the graph of the absolute value function f(x) = a|x - h| + k will have its lowest value when f(x) = k (or highest value for f(x) = -a|x - h| + k). The lowest/highest value is the vertex (turning point).

Therefore, from inspection of the equation we can say that the y-coordinate of the vertex is 5.

Set the equation to 5 and then solve for x:

⇒ 5 = 1/2 |-X – 4| + 5

⇒ 1/2 |-X – 4| = 0

⇒ |-X – 4| = 0

Therefore, (-X - 4) = 0 and -(-X - 4) = 0

⇒ X = -4 (for both)

So the vertex is (-4, 5)

Translations

Absolute value parent function: f(x) = | -x |

Horizontal translation left 4 units: f(x) = |-x - 4|

Horizontal stretch of sf 1/2: f(x) = 1/2 |-x - 4|

Vertical translation up 5 units: f(x) = 1/2 |-x - 4| + 5

6 0

3 years ago

Write the equation for the inverse of the function. y = sin x​

Write the equation for the inverse of the function. y = sin x