Answer:
77
Step-by-step explanation:Trust
Answer:
The inverse will be:
![y' = \frac{\sqrt{x+4}}{3}](https://tex.z-dn.net/?f=y%27%20%3D%20%5Cfrac%7B%5Csqrt%7Bx%2B4%7D%7D%7B3%7D)
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](https://tex.z-dn.net/?f=f%28x%29%20%20%3D%209x%5E%7B2%7D%20-%204)
![y = 9x^{2} - 4](https://tex.z-dn.net/?f=y%20%3D%209x%5E%7B2%7D%20-%204)
![x = 9y' ^{2} - 4](https://tex.z-dn.net/?f=x%20%3D%209y%27%20%5E%7B2%7D%20-%204)
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](https://tex.z-dn.net/?f=x%20%2B%204%3D%209y%27%5E%7B2%7D%20-%204%2B4)
= x + 4
Second divide by 9
/9 = (x + 4)/9
= (x + 4)/9
Now you will have to clear y, with the square root.
[/tex] =
Simplifying terms
![y' = \frac{\sqrt{x+4}}{3}](https://tex.z-dn.net/?f=y%27%20%3D%20%5Cfrac%7B%5Csqrt%7Bx%2B4%7D%7D%7B3%7D)
![f^{-1}(x) = \frac{\sqrt{x+4}}{3}](https://tex.z-dn.net/?f=f%5E%7B-1%7D%28x%29%20%20%3D%20%5Cfrac%7B%5Csqrt%7Bx%2B4%7D%7D%7B3%7D)
You can check the answer by doing the evaluation of the following equation:
(f o
) (x)
substitute the equation for y' or inverse function ![f^{-1}](https://tex.z-dn.net/?f=f%5E%7B-1%7D)
f(
)
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](https://tex.z-dn.net/?f=%3D%209%28%5Cfrac%7B%5Csqrt%7Bx%2B4%7D%20%7D%7B3%7D%7D%20%29%5E%7B2%7D%20%20-%204%5C%5C%5C%5CSolving%5C%5C%5C%5C9%28%5Cfrac%7B%7Bx%2B4%7D%20%7D%7B9%7D%7D%20%29%20%20-%204)
=x
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$70.88
x/67.5=5/100
cross multiply
100x=337.5
divide 100
x=3.375 or 3.38
67.50+3.38= 70.88