Question

If $f(x)=ax+b$ and $g(x)=cx+d$, then $f\{g(x)\}=g\{f(x)\}$ is equivalent to

• A. $f(a)=f(c)$
• B. $f(b)=g(b)$
• C. $f(d)=g(b)$
• D. $f(c)=g(a)$

Answer 1

Answer: (C)

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