Good morning everyone! Can someone please tell me if the answer I got for this question is correct. I'm not sure and I wanna mak
e sure it's right. If it's not then please give me the correct answer.
Please use the following image in order to answer the question correctly.
Find the measure of the red arc or angle.
What is the degree measurement of PS?(The symbol is in the image below)
Please show all the work on how you got your answer.(If you don't have an explanation then don't worry about it, just show your work on how you got the answer)
Please use the following image in order to answer the question correctly.
Find the measure of the red arc or angle.
What is the degree measurement of PS?(The symbol is in the image below)
Please show all the work on how you got your answer.(If you don't have an explanation then don't worry about it, just show your work on how you got the answer)
1 answer:
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Answer:
The functions are inverses; f(g(x)) = x ⇒ answer D
⇒ answer D
Step-by-step explanation:
* <em>Lets explain how to find the inverse of a function</em>
- Let f(x) = y
- Exchange x and y
- Solve to find the new y
- The new y =
* <em>Lets use these steps to solve the problems</em>
∵
∵ f(x) = y
∴
- Exchange x and y
∴
- Square the two sides
∴ x² = y - 3
- Add 3 to both sides
∴ x² + 3 = y
- Change y by
∴
∵ g(x) = x² + 3
∴
∴ <u><em>The functions are inverses to each other</em></u>
* <em>Now lets find f(g(x))</em>
- To find f(g(x)) substitute x in f(x) by g(x)
∵
∵ g(x) = x² + 3
∴
∴ <u><em>f(g(x)) = x</em></u>
∴ The functions are inverses; f(g(x)) = x
* <em>Lets find the inverse of h(x)</em>
∵ h(x) = 3x² - 1 where x ≥ 0
- Let h(x) = y
∴ y = 3x² - 1
- Exchange x and y
∴ x = 3y² - 1
- Add 1 to both sides
∴ x + 1 = 3y²
- Divide both sides by 3
∴
- Take √ for both sides
∴ ±
∵ x ≥ 0
∴ We will chose the positive value of the square root
∴
- replace y by
∴