The range of a function is the set of all possible values of the function. If the function f is defined by $f(x) = \frac{1}{x^2 + 1}$ for all real numbers x, the range of f is the set of

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all real numbers

all real numbers except -1 and 1

all positive real numbers

all real numbers greater than or equal to 0 and less than or equal to 1

all positive real numbers less than or equal to 1

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Explanation

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Official Explanation

Official

x^2

is always non-negative. Hence,

x^2+1

is always greater than or equal to 1.

If

x^2 + 1 = 1

→

\frac{1}{x^2 + 1} = 1

. This is the maximum possible value of f(x).…

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What this question tests

Your ability to evaluate and compose functions, including unusual defined operations.

Applying function operations in the wrong order or ignoring domain restrictions.