SOLUTION: Use the pair of functions to find f(g(x)) and g(f(x)) . Simplify your answers. f(x)=sqrt(x)+8,g(x)=x^2+3 f(g(x))= g(f(x))=

Question 1205886: Use the pair of functions to find f(g(x))
and g(f(x))
. Simplify your answers.
f(x)=sqrt(x)+8,g(x)=x^2+3

f(g(x))=
g(f(x))=
Found 2 solutions by MathLover1, Theo:
Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website!

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
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.

https://www.youtube.com/watch?v=QXGQtkbyFTs

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.

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