Q. If $f(x) = ax + b$ and $g(x) = cx + d$, then $f\left\{ g(x) \right\} = g\{ f(x)\}$ is equivalent to
A) $f(a) = f(c)$
B) $f(b) = g(b)$
C) $f(d) = g(b)$
D) $f(c) = g(a)$
Explanation
(c)
Given, $f(x) = ax + b,\ \ \ \ g(x) = cx + d$
$\because\ \ \ \ \ \ \ \ f\left\{ g(x) \right\} = g\{ f(x)\}$
$\Rightarrow \ \ \ f(cx + d) = g(ax + b)$
$\Rightarrow \ \ \ a(cx + d) + b = c(ax + b) + d$
$\Rightarrow \ \ \ \ \ \ \ \ ad + b = bc + d$
$\Rightarrow \ \ \ \ \ \ \ \ \ \ \ f(d) = g(b)$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.