Question 1205886
f(x) = sqrt(x) + 8
g(x) = x^2 + 3


to find f(g(x)), replace x in f(x) with g(x) to get:
f(g(x)) = sqrt(g(x)) + 8
since g(x) = x^2 + 3, you get:
f(g(x)) = sqrt(x^2 + 3) + 8


when x = 3, you get:
f(g(x)) = sqrt(3^2 + 3) + 8 = 11.46410162


this is equivalent to finding g(x) first and then finding f(g(x)).
g(x) = x^2 + 3.
when x = 3, g(x) = 3^2 + 3 = 12.
f(g(x)) becomes f(12) = sqrt(12) + 8 = 11.46410162.


f(x) and g(x) are repeated here to make them easier to reference.


f(x) = sqrt(x) + 8
g(x) = x^2 + 3


to find g(f(x)), replace x in g(x) with f(x) to get:
g(f(x)) = f(x)^2 + 3
since f(x) = sqrt(x) + 8, you get:
g(f(x)) = (sqrt(x) + 8)^2 + 3


when x = 3, you get:
g(f(x)) = (sqrt(3) + 8)^2 + 3 = 97.71281292.


this is equivalent to finding f(x) first and then finding g(f(x)).
f(x) = sqrt(x) + 8
when x = 3, f(x) = sqrt(3) + 8 = 9.732050808.
g(f(x)) becomes g(9.732050808) = 9.732050808^2 + 3 = 97.71281292.


your solution is:


f(g(x)) = sqrt(x^2 + 3) + 8


g(f(x)) = (sqrt(x) + 8)^2 + 3


here's a reference on composite functions.


<a href = "https://www.youtube.com/watch?v=QXGQtkbyFTs" target = "_blank">https://www.youtube.com/watch?v=QXGQtkbyFTs</a>


there are more videos on youtube regarding composition of functions, so feel free to look for others if looking at one is insufficient.
this particular tutor is pretty good as far as i can tell.