Relations and Functions — MATHS STD 11 Science — Question
Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSRelations and Functions1 Mark
Question
Find the domain and range of the real function: f(x) = - |x|
✓
Answer
Here the given function is: f(x) = -|x| As we know that, $\begin{equation} |\mathrm{X}|=\left\{\begin{array}{l} {\mathrm{x}, \text { if } \mathrm{x} \geq 0} \\ {-\mathrm{x}, \text { if } \mathrm{x}<0} \end{array}\right. \end{equation}$ $\begin{equation} f(x)=-|x|=\left\{\begin{array}{l} {-x, \text { if } x \geq 0} \\ {x, \text { if } x<0} \end{array}\right. \end{equation}$ Domain: The values that can be put in the function to obtain real value. For example f(x) = x, now we can put any value in place of x and we will get a real value. Hence, the domain of this function will be Real Numbers. Range: The values that we obtain of the function after putting the value from the domain. For Example: f(x) = x + 1, now if we put x = 0, f(x) = 1 . This 1 is a value of Range that we obtained. Since, f(x) is defined for x $\in$ R, the domain of f is R. It can be observed that the range of f(x) = -|x| is all real numbers except positive real numbers. Because we will always get a negative number when we put a value from a domain. Thus, the range of function is f(x) is (-$\infty$, 0]
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