Given that f(x) = x^k where k < 0, what is the range of f(x) on the interval [1, ∞)? Please explain, I want to understand how the answer is gotten. Thank you

EpicWater Dec 7, 2019

#1**+1 **

Given that f(x) = x^k where k < 0, what is the range of f(x) on the interval [1, ∞)? Please explain, I want to understand how the answer is gotten.

Ok, I will try to explain.

\( f(x) = x^k \;\;\;where\;\;\; k < 0, \;\;\:and \;\;\;\ x\ge1\\ let\;\; n=-k \;\;\;so\;\;\;n>0\\ f(x) = x^{-n}=\frac{1}{x^n}\\ now\;\; x\ge1 \;\; and\;\; n>0\;\;\;\\so\\ x^n\ge1\\ so\\ 0< \frac{1}{x^n} \le1\\ 0< x^{-n}\le1\\ 0< x^{k}\le1\\ \)

Here is the graph

Melody Dec 7, 2019