Question

Select the correct statements for the function $f\left(x\right)=|x|.$

• A. There will be one solution of equation $f\left(x\right)=a,a<0$
• B. There will be two solution of the equation $f\left(x\right)=a,a>0$
• C. Range $=[0,\infty )$
• D. Domain $=(-\infty ,\infty )$

Answer 1

Answer: (B), (C), (D)

Domain $=(-\infty ,\infty )$

Given the graph of the modulus function $f\left(x\right)=|x|$ as:

Now, based on the image, we get:
Domain of $f\left(x\right)$ as $x\in (-\infty ,\infty )$
And $f\left(x\right)\ge 0\forall x\in (-\infty ,\infty )$
$\therefore$ Range is given as: $f\left(x\right)\in [0,\infty )$
Also, for any positive number $a,a>0$
The function $y=f\left(x\right)$ cuts $y=a$ at two points as shown:
Also, for any number $a<0,f\left(x\right)=|a|$ will have no solutions.