+0

# Algebra 2 Repost Since the First One was Off-Topic

+1
56
3
+163

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

Dec 7, 2019

#1
+106933
+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

https://www.desmos.com/calculator/y0xfckw4zn

Dec 7, 2019
#2
+163
+1

Thank you so much, Melody. I understand this problem.

Dec 8, 2019
#3
+106933
0

You are very welcome EpicWaters.

Melody  Dec 8, 2019