Question

If $f^{\prime }(x)=g(x)$ and $g^{\prime }(x)=-f(x)$ for all x and $f(1)=5,f^{\prime }(1)=4,$ then the value of $f^2(1)+g^2(1)$ is equal to

• A. $25$
• B. $16$
• C. $41$
• D. $9$

Answer 1

Answer: (C)

Given, $f(1)=5$ and $g(x)=f^{\prime }(x)$ and $f^{\prime }(1)=4$
$\therefore$ $f^2(1)+g^2(1)={(5)}^2+{[f^{\prime }(1)]}^2$
$=25+{(4)}^2$ $=25+16$
$=41$