The domain and inverse of the function
is
Domain =
,
![r^{-1}(x) = \pm \sqrt{\frac{11}{x}} + 4](https://tex.z-dn.net/?f=r%5E%7B-1%7D%28x%29%20%3D%20%5Cpm%20%5Csqrt%7B%5Cfrac%7B11%7D%7Bx%7D%7D%20%2B%204)
What is a function?
A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.
There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.
The given function is
![r(x) = \frac{11}{(x - 4)^2}](https://tex.z-dn.net/?f=r%28x%29%20%3D%20%5Cfrac%7B11%7D%7B%28x%20-%204%29%5E2%7D)
r(x) is not defined if x - 4 = 0
r(x) is not defined for x = 4
Domain =
,
Where
is the set of all real number
Let r(x) = y
![\frac{11}{(x-4)^2} = y\\(x - 4)^2 = \frac{11}{y}\\x - 4 = \pm \sqrt{\frac{11}{y}}\\x = \pm\sqrt{\frac{11}{y}} +4](https://tex.z-dn.net/?f=%5Cfrac%7B11%7D%7B%28x-4%29%5E2%7D%20%3D%20y%5C%5C%28x%20-%204%29%5E2%20%3D%20%5Cfrac%7B11%7D%7By%7D%5C%5Cx%20-%204%20%3D%20%5Cpm%20%5Csqrt%7B%5Cfrac%7B11%7D%7By%7D%7D%5C%5Cx%20%3D%20%5Cpm%5Csqrt%7B%5Cfrac%7B11%7D%7By%7D%7D%20%20%2B4)
<em />![r^{-1}(x) = \pm \sqrt{\frac{11}{x}} + 4](https://tex.z-dn.net/?f=r%5E%7B-1%7D%28x%29%20%3D%20%5Cpm%20%5Csqrt%7B%5Cfrac%7B11%7D%7Bx%7D%7D%20%2B%204)
To learn more about function, refer to the link:
brainly.com/question/22340031
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