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