Question

Let $f$ and $g$ be defined by $f\left(x\right)=\sqrt{x}$ and $g\left(x\right)=x-1$ then

• A. $fog$ is continuous on $[0,\infty )$
• B. $gof$ is continuous on $[0,\infty )$
• C. $fog$ is continuous on $[1,\infty ]$
• D. none of these

Answer 1

Answer: (B), (C)

$gof$ is continuous on $[0,\infty )$
$fog$ is continuous on $[1,\infty ]$

For $f\left(x\right)=\sqrt{x}$ and $g\left(x\right)=x-1$
$fog\left(x\right)=\sqrt{x-1}$
Is defined when $x-1\ge 0\Rightarrow x\ge 1$
Hence continuous when $xϵ[1,\infty )$
And $gof\left(x\right)=\sqrt{x}-1$
Is defined for $x\ge 0$
Therefore, continuous when $xϵ[0,\infty )$
Hence, options 'B' and 'C' are correct.