1. Tardigrade
  2. Question
  3. Mathematics
  4. If f(x)=a x+b and g(x)=c x+d, then f g(x) =g f(x) is equivalent to

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. If $f(x)=a x+b$ and $g(x)=c x+d$, then $f\{g(x)\}=g\{f(x)\}$ is equivalent to

NTA AbhyasNTA Abhyas 2022Relations and Functions - Part 2

Solution:

Given, $f(x)=a x+b, g(x)=c x+d$
$\because f\{g(x)\}=g\{f(x)\} $
$\Rightarrow f(c x+d)=g(a x+b) $
$\Rightarrow a(c x+d)+b=c(a x+b)+d $
$\Rightarrow a d+b=b c+d $
$\Rightarrow f(d)=g(b)$