Given:
The function is:
To find:
The inverse of the given function, then draw the graphs of function and its inverse.
Solution:
We have,
Step 1: Substitute 
.
Step 2: Interchange x and y.
Step 3: Isolate variable y.
Step 4: Substitute 
.
Hence, the inverse of the given function is and the graphs of these functions are shown below.
In the inverse we replace the place of x by y .
![g(x) = \sqrt[3]{x} - 3 \\ \\ x = \sqrt[3]{y} - 3 \\ \sqrt[3]{y} = x + 3 \\ y = {(x + 3)}^{3} \\ y = {(x + 3)}^{2} (x + 3) \\ y = ({x}^{2} + 6x + 9)(x + 3) \\ \\ y = {x}^{3} + 6 {x}^{2} + 9x + 3 {x}^{2} + 18x + 27 \\ \\ y = {x}^{3} + 9 {x}^{2} + 27x + 27 \\ \\ \\ g(x)^{ - 1} = {x}^{3} + 9 {x}^{2} + 27x + 27](https://tex.z-dn.net/?f=g%28x%29%20%3D%20%20%5Csqrt%5B3%5D%7Bx%7D%20%20-%203%20%5C%5C%20%20%5C%5C%20x%20%3D%20%20%5Csqrt%5B3%5D%7By%7D%20%20-%203%20%5C%5C%20%20%5Csqrt%5B3%5D%7By%7D%20%20%3D%20x%20%2B%203%20%5C%5C%20y%20%3D%20%20%7B%28x%20%2B%203%29%7D%5E%7B3%7D%20%20%5C%5C%20y%20%3D%20%20%7B%28x%20%2B%203%29%7D%5E%7B2%7D%20%28x%20%2B%203%29%20%5C%5C%20y%20%3D%20%20%28%7Bx%7D%5E%7B2%7D%20%20%2B%206x%20%2B%209%29%28x%20%2B%203%29%20%5C%5C%20%5C%5C%20%20y%20%3D%20%20%7Bx%7D%5E%7B3%7D%20%20%2B%206%20%7Bx%7D%5E%7B2%7D%20%20%2B%209x%20%2B%203%20%7Bx%7D%5E%7B2%7D%20%20%2B%2018x%20%2B%2027%20%5C%5C%20%20%5C%5C%20y%20%3D%20%20%7Bx%7D%5E%7B3%7D%20%20%2B%209%20%7Bx%7D%5E%7B2%7D%20%20%2B%2027x%20%2B%2027%20%5C%5C%20%20%20%5C%5C%20%5C%5C%20g%28x%29%5E%7B%20-%201%7D%20%20%3D%20%20%7Bx%7D%5E%7B3%7D%20%20%2B%209%20%7Bx%7D%5E%7B2%7D%20%20%2B%2027x%20%2B%2027%20)
I hope I helped you^_^
Answer:
length = 24 meters
Step-by-step explanation:
1. l = 2w
2. P = 2l + 2w
P=72
3. 72 = 2l + 2w
4. Substitute w=l/2 to solve for l
72 = 2l + 2(l/2) ---> 72 = 3L - Divide by 3 on both sides
L= 24 meters
Answer:square root of 208
Step-by-step explanation: the difference of the X values is 8 and the diff of Y values is 12. 8 squared is 64 and 12 squared is 144. If both are added and square rooted, then it becomes sqrt 208
