Question

$Letf:[0,\sqrt{3}]\to [0,\frac{\pi }{3}+lo{g}_{e}2]definedf\left(x\right)=lo{g}_e\sqrt{x^2+1}+ta{n}^{-1}xthenf\left(x\right)is$

• A. one – one and onto
• B. one – one but not onto
• C. onto but not one – one
• D. neither one – one nor onto

Answer 1

The correct option is A

one – one and onto

$f^{\prime }\left(x\right)=\frac{x+1}{x^2+1}\Rightarrow f\left(x\right)isincreasingin[0,\sqrt{3}]$, So it is one one function.
and since range is equal to codomain, it is onto.