How would I start both of these questions not sure.

If h(x)=1/(x+3)^3 then determine

a. f(x) and g(x) such that h(x)=(f of g)(x).

b. r(x) and s(x)different from f(x) and g(x)such that h(x)=(r of s)(x)

I did part a) here

http://www.jiskha.com/display.cgi?id=1487781971

Thank you I just found notes on how to decompose a function. But I have 1 more question. For part B the problem would the problem be the same and you just use r(x) and s(x). I also notice that it says that they are different from f(x) and g(x).

To start solving both of these questions, you need to understand the concept of function composition. Function composition is a process where you take the output of one function and use it as the input for another function.

a. To determine f(x) and g(x) such that h(x) = (f of g)(x), you need to find two functions, f(x) and g(x), that when composed together, give you the function h(x).

Here's how you can approach it:

Step 1: Start with h(x) = 1/(x+3)^3.

Step 2: Let's assume g(x) is a function that transforms x to (x+3), i.e., g(x) = x + 3.

Step 3: Now, let's assume f(x) is a function that transforms x to 1/x^3, i.e., f(x) = 1/x^3.

Step 4: Define the composition (f of g) as f(g(x)), which means you substitute g(x) into f(x).

So, (f of g)(x) = f(g(x)) = f(x + 3) = 1/(x + 3)^3.

Therefore, the functions f(x) = 1/x^3 and g(x) = x + 3 satisfy h(x) = (f of g)(x).

b. To determine r(x) and s(x) different from f(x) and g(x) such that h(x) = (r of s)(x), you need to find two different functions, r(x) and s(x), that when composed together, give you the function h(x).

Here's how you can approach it:

Step 1: Start with h(x) = 1/(x+3)^3.

Step 2: Let's assume s(x) is a function that transforms x to (x+1), i.e., s(x) = x + 1.

Step 3: Now, let's assume r(x) is a function that transforms x to 1/x^3, i.e., r(x) = 1/x^3.

Step 4: Define the composition (r of s) as r(s(x)), which means you substitute s(x) into r(x).

So, (r of s)(x) = r(s(x)) = r(x + 1) = 1/(x + 1)^3.

Therefore, the functions r(x) = 1/x^3 and s(x) = x + 1 satisfy h(x) = (r of s)(x).