Question

If $f\left(x\right)=ax+b$ and $g\left(x\right)=cx+d$ such that $f\left(g\right(x\left)\right)=g\left(f\right(x\left)\right),$ then which one of the following is correct?

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

Answer 1

The correct option is D $f\left(d\right)=g\left(b\right)$

first of all we have to find $f\left(g\right(x\left)\right)$ = $a(cx+d)+b$

$f\left(g\right(x\left)\right)$ = $acx+ad+b$

and,

$g\left(f\right(x\left)\right)$ =$c(ax+b)+d$ = $cax+cb+d$

hence,

we get$f\left(d\right)=g\left(b\right)$