If $f(x)=e^{x}$, $g(x)=\ln (x)$ for all $x \in [1, \infty)$, then $f \circ g$ is ____

If $f(x)=e^{x}$, $g(x)=\ln (x)$ for all $x \in [1, \infty)$, then $f \circ g$ is ____
  1. A one-one function
  2. An onto function
  3. Not a function
  4. Bijective

Solution

For $x \in [1, \infty)$, $f(x)=e^{x}$ and $g(x)=\ln x$ $\therefore (f \circ g)(x)=e^{\ln x}=x$, $x \in [1, \infty)$ is a bijective function. Hence, option $(d)$ is correct.

Asked in: AP EAMCET 2020 (21 Sep Shift 1)

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