Question

Which of the following is/are true for function $f\left(x\right)=|{\log }_{e}x|$

• A. $f\left(x\right)$ is one-one function.
• B. $f\left(x\right)$ is many-one function.
• C. Domain of $f\left(x\right)$ is $(0,\infty )$
• D. Range of $f\left(x\right)$ is $[0,\infty )$

Answer 1

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

Range of $f\left(x\right)$ is $[0,\infty )$

$f\left(x\right)=|{\log }_{e}x|$


We can see from the graph that $f\left(x\right)=|{\log }_{e}x|$ is a many - one function as it gives same value of $y$ for different values of $x$
Domain of $f\left(x\right)=|\log x|$ is $(0,\infty )$
Range of $f\left(x\right)=|\log x|$ is $[0,\infty )$