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

Answer:The domain and range of the given function are  [tex](-\infty,+\infty)[/tex] and [tex](4,+\infty)[/tex]Solution:Given, function is f(x) = [tex]113(x-5)^{2}+4[/tex]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 [tex]-\infty[/tex] to [tex]+\infty[/tex]Domain of f(x) =  [tex](-\infty,+\infty)[/tex]Now, we need to find the range of f(x).f(x) = [tex]113(x-5)^{2}+4[/tex] .Here, x is in square term (i.e. [tex](x-5)^{2}[/tex] )So for any range of values of x, the value of [tex](x-5)^{2}[/tex] will always be in the range of 0 to ∞Numerical term 113 which is product with [tex](x-5)^{2}[/tex] will have no effect on range.Because [tex]113 \times 0 = 0[/tex] and so the range of function is still 0 to ∞Second numerical term 4 which is in addition with [tex]113(x-5)^{2}[/tex] 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  [tex](-\infty,+\infty)[/tex] and [tex](4,+\infty)[/tex]