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

Relations and Functions - Part 2

Solution:

We have $f(x)=a x+b, g(x)=c x+d$
Therefore, $f \{ g ( x )\}= g \{ f ( x )\} \Leftrightarrow f ( cx + d )= g ( ax + b )$
$
\Leftrightarrow a(c x+d)+b=c(a x+b)+d
$
$
\Leftrightarrow ad + b = cb + d \Leftrightarrow f ( d )= g ( b )
$