Look at the domain first. The value of n^4 is non-negative (it's an even power) and can't be greater than 4 without making a negative argument to the square root. So n^4 is in [0,4] and 4-n^4 is also in [0,4].
The value of f(n) is the square root of a number from 0 to 4, so the result is a number from 0 to 2.
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For the domain, we must have n^4 ≤ 4, or -√2 ≤ n ≤ √2. On [-√2, √2] f(n) ranges from 0 to 2. Range is [0, 2]
The minimum value of a √ is 0.
The maximum value of 4 - n^4 is 4.
Therefore, the maximum value of f(n) is √4 = 2.
f(n) is continuous. Therefore, its range is [0, 2].
Look at the domain first. The value of n^4 is non-negative (it's an even power) and can't be greater than 4 without making a negative argument to the square root. So n^4 is in [0,4] and 4-n^4 is also in [0,4].
The value of f(n) is the square root of a number from 0 to 4, so the result is a number from 0 to 2.
The range of f is then [0,2].