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andrezito [222]
3 years ago
11

Which function has an inverse that is also a function?

Mathematics
1 answer:
aalyn [17]3 years ago
4 0

Answer: 1st, 3rd, and 4th functions

Step-by-step explanation:

Assuming k(x)=9x^2, all the other functions have inverses because they are linear, meaning they must be one-to-one.

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Design a sine function with the given properties:
Rom4ik [11]

Answer:

f(x)=3\sin\left(\frac{\pi}{12}\left(x-10\right)\right)+13.

Step-by-step explanation:

Given information:

Period = 24 hr

Maximum = 16 at t=16 hr.

Minimum = 10 at t=4 hr.

The general sin function is

y=A+\sin(B(x-C))+D        .... (1)

where, |A| is altitude, \frac{2\pi}{B} is period, C is phase shift and D is midline.

Period is 24 hr.

24=\dfrac{2\pi}{B}\Rightarrow B=\dfrac{\pi}{12}

Altitude is

A=\dfrac{Maximum-Minimum}{2}=\dfrac{16-10}{2}=3

D=\dfrac{Maximum+Minimum}{2}=\dfrac{16+10}{2}=13

The function is minimum at t=4 and maximum at t=16,phase shift is

C=\dfrac{16+4}{2}=10

Substitute these values in equation (1).

y=3\sin\left(\frac{\pi}{12}\left(x-10\right)\right)+13

Therefore, the required function is f(x)=3\sin\left(\frac{\pi}{12}\left(x-10\right)\right)+13.

8 0
3 years ago
What is the range of the function shown in the table?
algol [13]

Answer:

C

Step-by-step explanation:

The range of a function is going to be the output of the table. 3, 4, 5, and 6 are all outputs in the table. C is the correct answer.

Hope this helps you.

Have a nice day.

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Step-by-step explanation: I really don’t know

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