Final answer:
To find the values of the given function, we substitute the given values into the function expression and simplify. We evaluate each part separately to find f(a), f(-a), -f(a), f(a+h), f(a)f(h), and f(a+h) - f(a)h.
Step-by-step explanation:
To find the values of the given function, we substitute the given values into the function expression. Let's evaluate each part one by one:
(a) f(a): Substitute 'a' into the function expression. f(a) = 4a^2 + 7a - 9.
(b) f(-a): Substitute '-a' into the function expression. f(-a) = 4(-a)^2 + 7(-a) - 9.
(c) -f(a): Multiply f(a) by -1. -f(a) = -1(4a^2 + 7a - 9).
(d) f(a+h): Substitute 'a+h' into the function expression. f(a+h) = 4(a+h)^2 + 7(a+h) - 9.
(e) f(a)f(h): Multiply f(a) and f(h) together. f(a)f(h) = (4a^2 + 7a - 9)(4h^2 + 7h - 9).
(f) f(a+h) - f(a)h: Substitute 'a+h' into f(a) and f(a)h, and subtract them. f(a+h) - f(a)h = (4(a+h)^2 + 7(a+h) - 9) - (4a^2 + 7a - 9)h, if h ≠ 0.