Question

Let $f:(e,\infty )\to R$ be a function defined by $f\left(x\right)=\log \left(\log \right(\log x\left)\right)$, the base of the logarithm being $e$. Then,

• A. $f$ is one-one and onto
• B. $f$ is one-one but not onto
• C. $f$ is onto but not one-one
• D. the range of $f$ is equal to its domain

Answer 1

The correct option is A $f$ is one-one and onto

We can see from the graph of $y=\log \left(\log \right(\log \left(x\right)\left)\right)$ that $f\left(x\right)$ is one-one and onto in $(e,\infty )$