The average value of [tex]f(g(2x+8))[/tex] on the interval [-1, 4] is given by
[tex]\dfrac{f(g(2\cdot4+8))-f(g(2\cdot(-1)+8))}{4-(-1)}=\dfrac{f(g(16))-f(g(6))}5[/tex]
We have
[tex]g(16)=2\cdot16^2+16-3=525[/tex]
[tex]f(525)=525^2-6\cdot525+4=272479[/tex]
[tex]g(6)=2\cdot6^2+6-3=75[/tex]
[tex]f(75)=5179[/tex]
[tex]\implies\dfrac{f(g(16))-f(g(6))}5=53460[/tex]
