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jasmin2344
11.10.2019 •
Mathematics
What are the domain and range of the function f(x)=113(x-5)²+4
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Ответ:
The domain and range of the given function are
and ![(4,+\infty)](/tpl/images/0308/5425/e5f1a.png)
Solution:
Given, function is f(x) =![113(x-5)^{2}+4](/tpl/images/0308/5425/c4d55.png)
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](/tpl/images/0308/5425/8b154.png)
Domain of f(x) =![(-\infty,+\infty)](/tpl/images/0308/5425/3a2c4.png)
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)](/tpl/images/0308/5425/e5f1a.png)
Ответ: