Final answer:
To evaluate ƒ(a + h) one must replace 'x' with 'a + h' in the function rule and then expand and simplify. Without knowing the specific function rule, a concrete evaluation cannot be provided. Additionally, any domain constraints provided must be considered.
Step-by-step explanation:
To evaluate the function ƒ(a + h), we need to know the actual function rule for ƒ that we are supposed to use. Without the rule, we cannot give a specific answer. However, typically in mathematics and calculus, when asked to evaluate ƒ(a + h), we are looking at what happens to the function when we substitute a + h into the function in place of the variable x. This process is often associated with exploring the limit of a function as h approaches zero, which is foundational to the concept of a derivative.
For example, if the function ƒ(x) = x^2, then to evaluate ƒ(a + h) you would replace x with a + h: ƒ(a + h) = (a + h)^2. Then, you would expand and simplify:
- (a + h)^2
- = a^2 + 2ah + h^2
To simplify, we combine any like terms if possible, but in this case, with no other terms to combine with a^2, 2ah, and h^2, this would be our simplified function evaluated at a + h.
If you are asked to consider this function within certain domain constraints, like for 0 ≤ x ≤ 20, you would also keep those constraints in mind when evaluating your function.