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# Given that f(x)=x^k where k>0, what is the range of f(x) on the interval (1, infinity)?

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Given that f(x)=x^k where k>0, what is the range of f(x) on the interval (1, ∞)?

Jan 31, 2019
edited by Guest  Jan 31, 2019

#1
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This is how it informs you on how the anwer should look like.

This problem requires you to answer in interval notation. Please take some time to read this tip carefully.

Enter intervals using parentheses and square brackets, as you normally would in interval notation.

For example, 2

Positive infinity should be entered as inf and negative infinity should be entered as -inf.

So x≤3, which would be x∈(−∞,3] in interval notation, should be submitted as (-inf, 3].

Likewise, y>5, which would be y∈(5,∞) in interval notation, should be submitted as (5, inf).

Intervals should be joined using the letter "U" to denote union.

The U should be separated by spaces.

Intervals joined this way should be non-overlapping.

For example, (2, 3) U (4, 8) is the union of two intervals, and [2, 5) U (5, 7) U [10, 12] is the union of three intervals.

For the set of all real numbers, use (-inf, inf).

For intervals such as all real numbers except for x=0, which you might also write as x≠0, you should enter (-inf, 0) U (0, inf).

To include a single point, use curly braces. So z∈{1}∪[2,4) will be entered as {1} U [2,4).

Jan 31, 2019
#2
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The range is (1, ∞).

As f(x) = xk is monotonically increasing on (1, ∞), if the domain is (a,b) then (f(a), f(b)) should be the range.

f(1) = 1

f(∞) = ∞

So the range is (1, ∞).

:)

Feb 1, 2019