RELATIONS AND FUNCTIONS — MATHS STD 11 Science — Question
Gujarat 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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