Find functions f and g so that h(x) = (f ∘ g)(x).
h(x) = (6x - 14)8
Assuming you mean
h(x) = (6x-14)^8
then just make
f(x) =x^8
g(x) = 6x-14
that way
(f∘g)(x) = f(g(x)) = (g(x))^8 = (6x-14)^8
How to solve. If there is a square root
Well, to find functions f and g such that h(x) = (f ∘ g)(x) = (6x - 14)8, we need to break down the composition of functions.
Let's start by letting g(x) = 6x - 14.
This means that when we input x into g, we get the value 6x - 14 as the output.
Next, let's determine f.
We want f to take the output of g(x) and multiply it by 8.
So, f(x) = 8x.
Now, we can combine the functions to get h(x) = (f ∘ g)(x).
Therefore, h(x) = f(g(x)) = f(6x - 14) = 8(6x - 14).
And there you have it! The functions f and g that satisfy h(x) = (f ∘ g)(x) = (6x - 14)8 are f(x) = 8x and g(x) = 6x - 14.
To find the functions f and g such that h(x) = (f ∘ g)(x) = (6x - 14)8, we can break down the composition of functions step by step.
Let's start with the inner function g(x). Since we need to multiply (6x - 14) by 8, g(x) should simply be the function that multiplies any input by 8. So, g(x) = 8x.
Now, let's move on to the outer function f(x). We want f(g(x)) = (6x - 14)8. This means that f takes the output of g(x), which is 8x, and performs the operation (6x - 14)8.
To achieve this, f(x) needs to multiply the input by (6x - 14) and then multiply the result by 8. So, f(x) = 8(6x - 14).
By substituting the function f(x) and g(x) into h(x) = (f ∘ g)(x), we get:
h(x) = (f ∘ g)(x) = f(g(x))
h(x) = f(8x) = 8(6(8x) - 14)
h(x) = f(g(x)) = 8(48x - 14)
h(x) = (6x - 14)8
Therefore, the functions f(x) = 8(6x - 14) and g(x) = 8x satisfy the equation h(x) = (f ∘ g)(x) = (6x - 14)8.