What are the domain and range of the function f(x)=113(x-5)²+4

The domain and range of the given function are   and

Solution:

Given, function is f(x) =

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

Domain of f(x) =  

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