Answer:
\((fog)(6)=1161\)
Step-by-step explanation:
It is given that \(f(x)=x^2+5\) and \(g(x)=5x+4\), then \((fog)(x)\) can be written as:
\((fog)(x)=(5x+4)^2+5\)
Upon solving the above equation, we get
\((fog)(x)=25x^2+16+40x+5\)
\((fog)(x)=25x^2+40x+21\)
Now, \((fog)(6)\) can be written as:
\((fog)(6)=25(6)^2+40(6)+21\)
\((fog)(6)=900+240+21\)
\((fog)(6)=1161\)
Therefore, the value of \((fog)(6)\) is 1161.
