I am stuck on a question about composition functions. They want you to find f(g(x)) and g(f(x)) using the following numbers:
g(x)= 10x
f(x)= x (squared)+4
Those are not numbers, they are called functions.
First consider f{g(x)}
Substitute 10x for the x in the f(x) function.
f{g(x)} = 100 x^2 + 4
Now consider g{f(x)}
Substitute x^2 +4 for x in the g(x) function.
g{f(x)} = 10 (x^2 +4) = 10x^2 + 40
Thank you! i had those answers but they looked funny. Thanks again
To find f(g(x)), you need to substitute g(x) into the function f. The given functions are:
g(x) = 10x
f(x) = x^2 + 4
Let's start by finding f(g(x)):
Step 1: Replace x in f(x) with g(x):
f(g(x)) = (g(x))^2 + 4
Step 2: Replace g(x) with its definition:
f(g(x)) = (10x)^2 + 4
Step 3: Simplify the expression:
f(g(x)) = 100x^2 + 4
Therefore, f(g(x)) = 100x^2 + 4.
Now, let's find g(f(x)):
Step 1: Replace x in g(x) with f(x):
g(f(x)) = 10(f(x))
Step 2: Replace f(x) with its definition:
g(f(x)) = 10[(x^2 + 4)]
Step 3: Simplify the expression:
g(f(x)) = 10x^2 + 40
Therefore, g(f(x)) = 10x^2 + 40.
So, f(g(x)) = 100x^2 + 4 and g(f(x)) = 10x^2 + 40.