Question

If $f\left(x\right)$ is a real valued function, then which of the following is one-one function?

• A. $f\left(x\right)=e^{|x|}$
• B. $f\left(x\right)=|e^x|$
• C. $f\left(x\right)=\sin x$
• D. $f\left(x\right)=|\sin x|$

Answer 1

The correct option is B $f\left(x\right)=|e^x|$

$\left(1\right)$ $f\left(x\right)=e^{|x|}$

Since$f\left(x\right)=f(-x)$

So $f\left(x\right)$ is many one.

$\left(2\right)$ $f\left(x\right)=|e^x|$

so, $f\left(x\right)=e^x$

and as $e^x$ is one-one

So $f\left(x\right)$ is one-one.

$\left(3\right)$ $f\left(x\right)=\sin x$

Since $\sin x$ is many one

So $f\left(x\right)$ is also many-one.

$\left(4\right)$ $f\left(x\right)=|\sin x|$

Since $\sin x$ is many one

So $f\left(x\right)$ is also many-one.