Answer:
Switch x and y, and solve for y
Step-by-step explanation:
Given
Required
Complete the steps to determine the inverse function
Solving (a): Complete the blanks
Switch x and y, and solve for y
Solving (b): Determine the inverse function
![f(x) = \sqrt[3]{8x} + 4](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%5Csqrt%5B3%5D%7B8x%7D%20%2B%204)
Replace f(x) with y
![y = \sqrt[3]{8x} + 4](https://tex.z-dn.net/?f=y%20%3D%20%5Csqrt%5B3%5D%7B8x%7D%20%2B%204)
Switch x and y
![x = \sqrt[3]{8y} + 4](https://tex.z-dn.net/?f=x%20%3D%20%5Csqrt%5B3%5D%7B8y%7D%20%2B%204)
<u>Now, we solve for y</u>
Subtract 4 from both sides
![x -4= \sqrt[3]{8y} + 4-4](https://tex.z-dn.net/?f=x%20-4%3D%20%5Csqrt%5B3%5D%7B8y%7D%20%2B%204-4)
![x -4= \sqrt[3]{8y}](https://tex.z-dn.net/?f=x%20-4%3D%20%5Csqrt%5B3%5D%7B8y%7D)
Take cube roots of both sides
Divide both sides by 8
So, we have:
Hence, the inverse function is:
<h3>
Answer: 10.99</h3>
Work Shown:
Angle B = 20 is the reference angle
AC = 4 is the side opposite this reference angle
BC = x is the unknown adjacent side
tan(angle) = opposite/adjacent
tan(B) = AC/BC
tan(20) = 4/x
x*tan(20) = 4
x = 4/tan(20)
x = 10.9899 approximately (make sure your calc is in degree mode)
x = 10.99 rounding to two decimal places
BC = 10.99
40/16 = 24/x
16*24 = 384
x = 384 / 40
x =9.6
it cast a shadow 9.6 feet long
Factor using the AC method...
The answer is:
(x+6) (x+8)
