Find functions f and g so that h(x) = (f ∘ g)(x).
h(x) = (6x - 14)8
(f ∘ g)(x) = f(g(x))
f(g(x)) = 8(6x - 14)
g(x) could be 6x - 14 and f(x) could be 8x
Thank you
Find (f°g)(-3). f(x)=4x. g(x)=x+4. (f°g)(-3)=
To find functions f and g such that h(x) = (f ∘ g)(x), we need to decompose h(x) into the composition of two functions, f and g.
Given that h(x) = (6x - 14)8, we can represent it as h(x) = f(g(x)).
Let's set f(g(x)) = (6x - 14)8 and work backward to find f and g.
Step 1: Identify g(x)
Looking at (6x - 14)8, we can see that g(x) = 6x - 14.
Step 2: Identify f(x)
Now we need to determine the function f that operates on the result of g(x).
We have f(g(x)) = (6x - 14)8.
Since the output of g(x) is (6x - 14), we can represent it as f((6x - 14)) = 8.
To isolate f, we can solve the equation f(a) = 8, where a = (6x - 14).
This means f(a) is a function that takes any input a and outputs 8.
A simple example of such a function would be f(a) = 8.
Therefore, we have g(x) = 6x - 14 and f(a) = 8.
Thus, the functions f and g such that h(x) = (f ∘ g)(x) are:
f(a) = 8
g(x) = 6x - 14.