Question

Let $f\left(x\right)=x+2$ and $g\left(x\right)=cx+d,c\ne 0$. If $\left(fog\right)\left(x\right)=\left(gof\right)\left(x\right)$ for all $x,$ then $c$ is

• A. 1
• B. 01
• C. 1.0
• D. 1.00

Answer 1

Answer: (A), (B), (C), (D)

$\left(fog\right)\left(x\right)=f\left(g\right(x\left)\right)=(cx+d)+2$ and $\left(gof\right)\left(x\right)=g\left(f\right(x\left)\right)=c(x+2)+d$
Given that $\left(fog\right)\left(x\right)=\left(gof\right)\left(x\right)$
$\Rightarrow cx+d+2=cx+2c+d\Rightarrow c=1$ and $d$ is any arbitrary constant.