Final answer:
To find the values of different expressions involving the given function, substitute the desired values in place of x and perform the calculations.
Step-by-step explanation:
a) To find f(2), substitute 2 for x in the function: f(2) = 5(2)^2 - 2 + 2 = 5(4) - 2 + 2 = 20 - 2 + 2 = 20
b) To find f(-2), substitute -2 for x: f(-2) = 5(-2)^2 - (-2) + 2 = 5(4) + 2 + 2 = 20 + 2 + 2 = 24
c) To find f(a), substitute a for x: f(a) = 5a^2 - a + 2
d) To find f(-a), substitute -a for x: f(-a) = 5(-a)^2 - (-a) + 2 = 5a^2 + a + 2
e) To find f(a+1), substitute a+1 for x: f(a+1) = 5(a+1)^2 - (a+1) + 2 = 5(a^2 + 2a + 1) - a - 1 + 2 = 5a^2 + 10a + 5 - a - 1 + 2 = 5a^2 + 9a + 6
f) To find 2f(a), multiply the function by 2: 2f(a) = 2(5a^2 - a + 2) = 10a^2 - 2a + 4
g) To find f(2a), substitute 2a for x: f(2a) = 5(2a)^2 - (2a) + 2 = 20a^2 - 2a + 2
h) To find f(a^2), substitute a^2 for x: f(a^2) = 5(a^2)^2 - (a^2) + 2 = 5a^4 - a^2 + 2
i) To find [f(a)], square the function: [f(a)] = [5a^2 - a + 2]^2 = 25a^4 - 10a^3 + 29a^2 - 4a + 4
j) To find f(a+h), substitute a+h for x: f(a+h) = 5(a+h)^2 - (a+h) + 2 = 5(a^2 + 2ah + h^2) - a - h + 2 = 5a^2 + 10ah + 5h^2 - a - h + 2