Chapter 10 - The Laplace Transform and Some Elementary Applications - 10.5 The First Shifting Theorem - True-False Review - Page 694: c

True

Plug $x=t+2 \implies t=x-2$ Now, $f(t+2)=\dfrac{e^{t}}{\sqrt {t+3}}$ and $f(x)=\dfrac{e^{x-2}}{\sqrt {x+1}}$ Replace $x$ with $t$ to obtain: $f(t)=\dfrac{e^{t-2}}{\sqrt {t+1}}$ Therefore, the given statement is $\bf{True}$.