find the functions f and g so that
Fog = H.
H(x)=/2x+1\
To find the functions f and g such that Fog = H, we need to understand the composition of functions. Let's break down the steps:
1. Start with the given function H(x) = (2x + 1).
2. Determine the inner function g(x) that will be applied first. In this case, g(x) needs to produce the input for the outer function f(x) so that H(x) = f(g(x)).
3. Let's choose g(x) = x.
4. Next, we need to find the function f(x) that will process the output of g(x) to give us H(x). To do this, we substitute g(x) into the original function, f(g(x)), and solve for f(x).
f(g(x)) = f(x) = (2g(x) + 1)
Substitute g(x) = x:
f(x) = (2x + 1)
5. Now we have the functions f(x) = (2x + 1) and g(x) = x where H(x) = f(g(x)).
So, the functions f and g that satisfy Fog = H, where H(x) = (2x + 1), are f(x) = (2x + 1) and g(x) = x.