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Maksim231197 [3]
3 years ago
8

Which equation is the inverse of y = 9x2 - 4?

Mathematics
1 answer:
m_a_m_a [10]3 years ago
5 0

Answer:

The inverse will be:

y' = \frac{\sqrt{x+4}}{3}

Step-by-step explanation:

In order to find the inverse of the equation, we do a variable change, since we are finding the inverse, :

f(x)  = 9x^{2} - 4

y = 9x^{2} - 4

x = 9y' ^{2} - 4

Now solve for y'.

First add 4 in both sides of the equation and change to the left y'.

x + 4= 9y'^{2} - 4+4

9y'^{2} = x + 4

Second divide by 9

9y'^{2}/9 = (x + 4)/9

y'^{2} = (x + 4)/9

Now you will have to clear y, with the square root.

[tex]y'^{\frac{2}{2}} = \sqrt{x + 4}  / \sqrt{9}[/tex] =

Simplifying terms

y' = \frac{\sqrt{x+4}}{3}

f^{-1}(x)  = \frac{\sqrt{x+4}}{3}

You can check the answer by doing the evaluation of the following equation:

(f o f^{-1} ) (x)

substitute the equation for y' or inverse function f^{-1}

f(\frac{\sqrt{x+4} }{3})

Now substitue the value into f(x)

You will have

= 9(\frac{\sqrt{x+4} }{3}} )^{2}  - 4\\\\Solving\\\\9(\frac{{x+4} }{9}} )  - 4

=x

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Read 2 more answers
2.1 , - 6/10 , -9/4 , -0.75 , 5/3 , least to greatest
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-9/4, -0.75, -6/10, 5/3, 2.1

Step-by-step explanation:

This is a lot easier to figure out if you simplify the fractions and then change them to decimals

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-0.75

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2.1

When you are ordering negatives, the biggest negative is the least. That is why -9/4 (-2.25) is the least number out of the five given.

The next one would be -0.75, because it is the second biggest negative fraction.

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I hope this helped :)

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