Question

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

Answer 1

Answer:

The domain and range of the given function are  $(-\infty,+\infty)$ and $(4,+\infty)$

Solution:

Given, function is f(x) = $113(x-5)^{2}+4$

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 $-\infty$ to $+\infty$

Domain of f(x) =  $(-\infty,+\infty)$

Now, we need to find the range of f(x).

f(x) = $113(x-5)^{2}+4$ .Here, x is in square term (i.e. $(x-5)^{2}$ )

So for any range of values of x, the value of $(x-5)^{2}$ will always be in the range of 0 to ∞

Numerical term 113 which is product with $(x-5)^{2}$ will have no effect on range.

Because $113 \times 0 = 0$ and so the range of function is still 0 to ∞

Second numerical term 4 which is in addition with $113(x-5)^{2}$ 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  $(-\infty,+\infty)$ and $(4,+\infty)$