Given f(x) = 7x^2 - 5xf(x)=7x25x, g(x) = 17x - 4g(x)=17x4 how do you find (fog)(6)?

1 Answer
May 16, 2018

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

Explanation:

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

If color(blue)(g(color(red)x))=17color(red)x-4g(x)=17x4
then color(blue)(g(color(red)6))=17 * color(red)6 -4 = color(blue)(98)g(6)=1764=98

and if (fog)(color(blue)x)=f(color(blue)x)=7color(blue)x^2-5color(blue)x(fog)(x)=f(x)=7x25x
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))(fog)(x)=f(g(x))=7g(x)25g(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)=66738then (fg)(x)=f(g(6))=7982598=66738
(I used a calculator for the last evaluation)