Question

Given `f(x) = 7x^2 - 5x`, `g(x) = 17x - 4` how do you find (fog)(6)?

Answer 1

`(fcircg)(6)=66,738`

Explanation:

`(fcircg)(x)` can be written as `f(color(blue)(g(color(red)x)))`

If `color(blue)(g(color(red)x))=17color(red)x-4`
then `color(blue)(g(color(red)6))=17 * color(red)6 -4 = color(blue)(98)`

and if `(fog)(color(blue)x)=f(color(blue)x)=7color(blue)x^2-5color(blue)x`
then `(fog)(color(blue)x)=f(color(blue)(g(color(red)x)))=7color(blue)(g(color(red)x))^2-5color(blue)(g(color(red)x))`
and
`color(white)("then ")(fcircg)(color(blue)x)=f(color(blue)(g(color(red)6)))=7 * color(blue)(98)^2 - 5 * color(blue)(98)=66738`
(I used a calculator for the last evaluation)