Q. If $f(x) = e^{x}$ and $g(x) = \log_{e}x$, then which of the following is true?
A) $f\{ g(x)\} \neq g\{ f(x)\}$
B) $f\left\{ g(x) \right\} = g\{ f(x)\}$
C) $f\left\{ g(x) \right\} + g\left\{ f(x) \right\} = 0$
D) $f\left\{ g(x) \right\} - g\left\{ f(x) \right\} = 1$
Explanation
(b)
Given,
$\ \ \ \ \ \ \ \ \ \ f(x) = e^{x}$ and $g(x) = \log_{e}x$
Now, $f\left\{ g(x) \right\} = e^{\log_{e}x} = x\$
And $g\left\{ f(x) \right\} = \log_{e}e^{x} = x$
$\therefore\ \ f\{ g(x)\} = g\{ f(x)\}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.