Question

Let $f\left(x\right)=|x^2-1|,$ then in which of the following interval(s) $f\left(x\right)$ is one-one function

• A. $[1,\infty )$
• B. $(0,\infty )$
• C. $[-1,\infty )$
• D. $[0,1]$

Answer 1

Answer: (A), (D)

$[0,1]$

Graph of $f\left(x\right)=|x^2-1|$ is ,


Using horizontal line test in the above obtained graph of $f\left(x\right)=|x^2-1|$ and from the given options, we can observe that $f\left(x\right)$ is one one function individually in the intervals $[1,\infty ),[0,1]$