Express the function in the form f o g. (Use non-identity functions for f and g.)
G(x)= cube root of (x/(9+x))
{f(x),g(x)}=?
Well, thank you for the math question! Let me juggle some functions and come up with the answer for you. How about we use f(x) = sin(x) and g(x) = ln(x)?
So, {f(x), g(x)} = {sin(x), ln(x)}.
To express the function G(x) in the form f o g, we need to find two functions, f(x) and g(x), such that G(x) = f(g(x)). Let's break down the process step by step.
Step 1: Identify the function g(x)
The function g(x) will be the inner function, meaning it will take an input value and transform it in some way to produce an intermediate result. In this case, we can choose g(x) = x/(9+x).
Step 2: Identify the function f(x)
The function f(x) will be the outer function, which takes the intermediate result of g(x) and further transforms it to produce the final result, which is G(x). We need to express G(x) in terms of g(x) and find the relationship between them.
G(x) = cube root of (x/(9+x))
To express G(x) in terms of g(x), we can rewrite G(x) as:
G(x) = cube root of g(x)
In this case, the function f(x) is simply taking the cube root of its input, which is the intermediate result g(x).
Therefore, the expression in the form f o g is:
{f(x), g(x)} = {cube root of x, x/(9+x)}
Express the function in the form
f ∘ g.
(Use non-identity functions for f and g.)
F(x) =
3
x
9 +
3
x
g(x) = x/(9+x)
f(x) = ∛x