If f(x) is a function such that $f^{\prime \prime }\left(x\right)+f\left(x\right)=0$ and $g\left(x\right)=\left(f\right(x){)}^2+{\left(f^{\mathrm{\prime }}\left(x\right)\right)}^2$ and $g\left(3\right)=3\text{ then }g\left(8\right)=$

$g\left(x\right)=\left(f\right(x){)}^2+{\left(f^{\mathrm{\prime }}\left(x\right)\right)}^2$

$g^{\mathrm{\prime }}\left(x\right)=2f\left(x\right)f^{\mathrm{\prime }}\left(x\right)+2f^{\mathrm{\prime }}\left(x\right)f^{\prime \prime }\left(x\right)$

$g\text{'}\left(x\right)=2f^{\mathrm{\prime }}\left(x\right)\left(f^{\prime \prime }\left(x\right)+f\left(x\right)\right)$

$g\text{'}\left(x\right)=2f^{\mathrm{\prime }}\left(x\right(0)=0$

$\therefore g$ is constant

$g\left(3\right)=3\text{ then }g\left(8\right)=3$