Given that f(x) = -x + 4 and g(x) = -2x - 3, solve for f(g(x)) when x = 2.

Solution:

g(x) =  - 2x - 3 ….. (1)

f(x) = - x + 4 ….. (2)

f(g(x)) can be written as (fog)(x) which is a composite function.

f(g(x)) takes the input values of g(x). 

I.e., substituting equation (1) in x which is present in equation (2)

f(g(x)) =  f(-2x - 3)                                   

f(g(x)) = - (- 2x - 3) + 4

f(g(x)) = 2x + 3 + 4

f(g(x)) = 2x + 7

Now substitute x = 2 in f (g(x))

f(g(x)) = 2 (2) + 7

So we get

f(g(x)) = 4 + 7 = 11

Therefore, f(g(x)) when x = 2 is 11.

Given that f(x) = -x + 4 and g(x) = -2x - 3, solve for f(g(x)) when x = 2.

Summary:

Given that f(x) = -x + 4 and g(x) = -2x - 3, f(g(x)) when x = 3 is 11.