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Question
Find the domain and range of the real valued function:
(vii) \[f\left( x \right) = - \left| x \right|\]
Solution
f (x) = – | x |, x ∈ R
We know that
\[\left| x \right| = \begin{cases}x, & x \geq 0 \\ - x & x < 0\end{cases}\]
Since f(x) is defined for x ∈ R, domain of f = R.
It can be observed that the range of f (x) = – | x | is all real numbers except positive real numbers.
∴ The range of f is (– ∞, 0).
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