Final answer:
To find f(x) in the equation (f o g)(x), where g(x) = (8 + x⁷)/(8 - x⁷) and h(x) = (8 + x⁷)/(8 - x⁷)², we substitute g(x) into h(x) and simplify. However, it is not possible to find a specific function f(x) that satisfies the equation.
Step-by-step explanation:
To find f(x) such that h(x) = (f o g)(x) and g(x) = (8 + x⁷)/(8 - x⁷), we need to substitute g(x) into h(x). Substituting, we get h(x) = ((8 + x⁷)/(8 - x⁷))². To find f(x), we simplify h(x) to obtain a function of x that does not involve f(x).
In this case, we simplify h(x) by multiplying the numerator and the denominator by its conjugate, where the conjugate of 8 - x⁷ is 8 + x⁷. By doing so, we get h(x) = ((8 + x⁷)²)/((8 - x⁷)²). Now, we have a simplified expression for h(x). However, this expression does not involve f(x).
Therefore, it is not possible to find a specific function f(x) such that h(x) = (f o g)(x). The given expression for g(x) cannot be further simplified or manipulated to isolate f(x).