Question

If f(x) = x^2-6x+4 and g(x) =2x^2+x-3, find the average rate of change of f(g(2x+8)) on the interval [-1,4]

Answer 1

The average value of
`f(g(2x+8))` on the interval [-1, 4] is given by

`(f(g(2\cdot4+8))-f(g(2\cdot(-1)+8)))/(4-(-1))=\frac{f(g(16))-f(g(6))}5`

We have

`g(16)=2\cdot16^2+16-3=525`

`f(525)=525^2-6\cdot525+4=272479`

`g(6)=2\cdot6^2+6-3=75`

`f(75)=5179`

`\implies\frac{f(g(16))-f(g(6))}5=53460`