Question

Let $f\left(x\right)=e^{2x+1}$ and $g\left(x\right)=\ln x.$ Then $(f\circ g)\left(x\right)$ is

[2 marks]

• A. $2x+e$
• B. $x^2$
• C. $e^{2x+e}$
• D. $e{x}^2$

Answer 1

The correct option is D $e{x}^2$

$f\left(x\right)=e^{2x+1}$ and $g\left(x\right)=\ln x$
$\Rightarrow (f\circ g)\left(x\right)=e^{2\ln x+1}$
$\Rightarrow (f\circ g)\left(x\right)=e^{\ln x^2}\cdot e$
$\Rightarrow (f\circ g)\left(x\right)=e{x}^2(\because e^{\ln t}=t)$