Final answer:
To find f(9) we evaluate the constant function f(x) = 9/2 at x=9, yielding 4.5. The function g(x) remains as g(x) = 8x + 13. The composition f(g(t)) is found by substituting g(t) into f(x), resulting in 9/2 * (8t + 13). The functions f(x) and g(x) are not inverses.
Step-by-step explanation:
When working with functions, to find f(9), we simply substitute 'x' with 9 in the function f(x). Since f(x) = 9/2 is a constant function, f(9) will also be 9/2, which in decimal form is 4.5. Therefore, f(9) = 4.5. The function g(x) is already given as g(x) = 8x + 13, so there is no need to find it, but just to confirm, it remains the same for any value of 'x'.
To find f(g(t)), we need to substitute g(t) into the function f(x). Since f(x) = 9/2, it means whatever we substitute in for 'x', we simply multiply 9/2 by that expression. Therefore, f(g(t)) = 9/2 * (8t + 13). It is a composition of function g into function f.
To determine if the two functions are inverses of each other, we look for a condition where composing one with the other gives us the identity function. This means f(g(x)) should equal x and g(f(x)) should equal x. Since neither f(g(x)) nor g(f(x)) simplifies to 'x', the functions are not inverses. So, the answer is False.