Question

Find functions f(x) and g(x) so the given function can be expressed as

H(x) = (f ∘ g)(x).
(Use non-identity functions for f(x) and g(x).

H(x)= sqrt((4x-1)/(5x+6))

Answer 1

4x - 1

Explanation:

To find functions f(x) and g(x) such that H(x) = (f ∘ g)(x), we need to decompose the given function H(x) into a composition of two functions. Let's start by expressing H(x) in terms of f(g(x)).

H(x) = sqrt((4x-1)/(5x+6))

To simplify this expression, we can break it down into two parts: f(x) and g(x).

Let's assign g(x) = 4x - 1 and f(x) = sqrt(x).

Now, we can express H(x) as (f ∘ g)(x):

H(x) = f(g(x)) = sqrt(g(x))

Substituting the value of g(x) into the expression, we get:

H(x) = sqrt(4x - 1)

Therefore, the functions f(x) = sqrt(x) and g(x) = 4x - 1 satisfy the condition H(x) = (f ∘ g)(x) for the given function.

Sorry if this seems confusing! You're welcome :]