Excellent question. It used to bother me too, until I developed a trick.Originally Posted byredier

Consider a function,

The range are all the values of such that there exists an in the domain such as,

.

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Example,

Find the range of,

The domain is all real numbers.

Thus, for what values of does the equation have a solution.

Say,

Then,

Thus,

Note this equation can only have a solution when the Left Hand side is non-negative. That is,

.

Thus,

If you solve this inequality (details omitted) you have that,

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As an excersce,

Find the range of,