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

$\dfrac{f(g(2\cdot4+8))-f(g(2\cdot(-1)+8))}{4-(-1)}=\dfrac{f(g(16))-f(g(6))}5$

We have

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

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

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

$f(75)=5179$

$\implies\dfrac{f(g(16))-f(g(6))}5=53460$