How do I find (fog)(x) with the given equations f(x)=8x+2 and g(x)=x^2-8 ?

Question

normally I would know hoe to solve this is a number was in the place of the x but since the x is there, I'm stuck.

Answer 1

f(x) = 8x + 2

g(x) = x² - 8

To take the composition of f and g (fog), replace the x in f(x) with g(x):

 

(fog)(x) = 8g(x) + 2                 [f(x) = 8x + 2]

 

(fog)(x) = 8(x² - 8) + 2            [since g(x) = x²-8]

 

(fog)(x) = 8x² - 64 + 2

 

(fog)(x) = 8x² - 62

 

For a primer on composition of functions, check out the following:

 

http://www.mathsisfun.com/sets/functions-composition.html

Answer 2

Sometimes shown as f(g(x))

Therefore look at the f(x) and put in the g(x) wherever the x in f(x) is

Then turn the algebraic crank