Not sure how to do this problem need a little help at least to start.
If h(x) = 1/(x+3)^3 then determine
f(x) and g(x) such that h(x) = (f of g)(x).
I read your (f of g)(x) as f( g(x) )
By the "Just look at it" theorem,
if g(x) = x+3
and f(x) = 1/x^3
then f(g(x))
= f(x+3)
= 1/(x+3)^3 , which is h(x)
Thanks for your help
To determine f(x) and g(x) such that h(x) = (f of g)(x), we need to break down the function h(x) into smaller functions. Let's look at the given function h(x) = 1/(x+3)^3.
We can start by decomposing the denominator, (x+3)^3. This can be written as f(x) = x+3 raised to the power of 3.
Next, we need to determine what operation g(x) performs on the input x. In this case, the function h(x) has a reciprocal operation, 1/x, applied to it. Therefore, g(x) = 1/x.
So, we have f(x) = (x+3)^3 and g(x) = 1/x.
Now, we can rewrite h(x) = 1/(x+3)^3 as (f of g)(x), which means that we substitute g(x) into f(x). Therefore, the final expression is h(x) = f(g(x)) = f(1/x) = ((1/x) + 3)^3.
Therefore, f(x) = (x+3)^3 and g(x) = 1/x, and h(x) = (f of g)(x) = ((1/x) + 3)^3.