find the f and g, so that fOg= H
H(x)=sqrt x^2+17
please show work
To find the functions f and g such that f∘g = H(x) = sqrt(x^2 + 17), we need to split the expression H(x) into two separate functions, f and g.
Let's start by defining g(x) = x^2 + 17, which represents the inner function. This choice is based on the fact that the expression inside the square root is x^2 + 17.
Now, we need to find f(x) such that f(g(x)) = f(x^2 + 17) gives us the final result H(x) = sqrt(x^2 + 17).
Since H(x) = sqrt(x^2 + 17), we can see that f(x) = sqrt(x) will give us the desired result. By substituting g(x) into f(x), we have f(g(x)) = f(x^2 + 17) = sqrt(x^2 + 17), which matches H(x).
Therefore, f(x) = sqrt(x) and g(x) = x^2 + 17.
To summarize:
f(x) = sqrt(x)
g(x) = x^2 + 17
f∘g = H(x) = sqrt(x^2 + 17)