Q. The function $f:(-\infty,\infty)\to(-\infty,1)$, defined by $f(x)=\frac{2^x-2^{-x}}{2^x+2^{-x}}$ is :
A) Neither one-one nor onto
B) Onto but not one-one
C) Both one-one and onto
D) One-one but not onto
Explanation
[Solution by Dr. Abubacker] $f(x)=\tanh(x\ln2)$ is strictly increasing, hence one-one, and its range is $(-1,1)$, which is not equal to the codomain $(-\infty,1)$. So $f$ is one-one but not onto. Answer (4).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.