<u>Answer:</u>
The domain and range of the given function are
and ![(4,+\infty)](https://tex.z-dn.net/?f=%284%2C%2B%5Cinfty%29)
<u>Solution:</u>
Given, function is f(x) = ![113(x-5)^{2}+4](https://tex.z-dn.net/?f=113%28x-5%29%5E%7B2%7D%2B4)
f(x) is a polynomial, so there exists no value of x, such that the function becomes undefined, which means the domain of the given function extends from
to ![+\infty](https://tex.z-dn.net/?f=%2B%5Cinfty)
Domain of f(x) = ![(-\infty,+\infty)](https://tex.z-dn.net/?f=%28-%5Cinfty%2C%2B%5Cinfty%29)
Now, we need to find the range of f(x).
f(x) =
.Here, x is in square term (i.e.
)
So for any range of values of x, the value of
will always be in the range of 0 to ∞
Numerical term 113 which is product with
will have no effect on range.
Because
and so the range of function is still 0 to ∞
Second numerical term 4 which is in addition with
will change the range of function.
Because, 0 + 4 = 4, and ∞ + 4 = ∞
So, the range of the given function f(x) is 4 to ∞
Hence the domain and range of the given function are
and ![(4,+\infty)](https://tex.z-dn.net/?f=%284%2C%2B%5Cinfty%29)