Final answer:
To solve for f(a), f(a+h), and the expression (f(a+h) - f(a))/h, one must substitute the variables into the function f(x) = -8 + 8x² and simplify. The calculations involve basic algebraic manipulation and substitution.
Step-by-step explanation:
The question asks to calculate values of the function f(x) = -8 + 8x² for f(a), f(a+h), and the expression (f(a+h) - f(a))/h. Let's break down the steps for each calculation.
Calculating f(a)
Simply substitute a for x in the function:
f(a) = -8 + 8a²
Calculating f(a+h)
Now substitute (a + h) for x:
f(a+h) = -8 + 8(a+h)²
= -8 + 8(a² + 2ah + h²)
Calculating the expression (f(a+h) - f(a))/h
Subtract f(a) from f(a+h) and divide by h:
((-8 + 8(a² + 2ah + h²)) - (-8 + 8a²))/h
= (8ah + 8h²)/h
= 8a + 8h