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Mathematics 19 Online
OpenStudy (18jonea):

Find the inverse of y = 3x2 + 4. Is the inverse a function?

OpenStudy (18jonea):

@Hero

hero (hero):

0. You are given \(y = 3x^2 + 4\) 1. Subtract 4 from both sides.

OpenStudy (18jonea):

-4 +y= 3x^2 @Hero

hero (hero):

2. Write it as \(y - 4 = 3x^2\) 3. Now divide both sides by 3.

OpenStudy (18jonea):

x^2 = 1/3y -4/3 @Hero

hero (hero):

4. Write it as \(\dfrac{y - 4}{3} = x^2\) 5. Next, square root both sides. and simplify. Remember \(\sqrt{a^2} = \pm a\)

OpenStudy (18jonea):

x= 2 sqrty/ sqrt 3

hero (hero):

6. If you take the square root of both sides, you should have: \(\pm\sqrt{\dfrac{y - 4}{3}} = x\)

hero (hero):

7. Swap \(x\) and \(y\).

OpenStudy (18jonea):

square root x-4 /3 =y

hero (hero):

8. If you write the result in horizontal form, you must use parentheses to clarify what expressions belong in the square root, what expressions belong in the denominator, numerator, etc. 9. Do not forget the plus/minus symbol. 10. The correct result for the inverse of the given equation is ±sqrt((x - 4)/(3)) = y

hero (hero):

11. The plus/minus symbol implies that for the resulting inverse equation, there are two outputs \(y\) for every input \(x\).

OpenStudy (18jonea):

so is it a funtion

hero (hero):

For a function, how many outputs should there be for each input?

OpenStudy (18jonea):

1

hero (hero):

So what can we conclude about the inverse of the given equation?

OpenStudy (18jonea):

it is a solution?

hero (hero):

12. The inverse of the given equation is not a function.

OpenStudy (18jonea):

@Hero

hero (hero):

Yes, that is correct.

OpenStudy (18jonea):

thank you can you help me with a couple more?

hero (hero):

Maybe

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