Consider the function f(x) = x^2 +2\sqrt{x}. Evaluate 2f(2) - f(8).

-56 + 3 sqrt(2) /2

Step-by-step explanation:

f(x) = x^2 +2/sqrt{x}.

2f(2) - f(8).

First find f(2)

f(2) = 2^2 +2/sqrt{2} = 4 + 2/ sqrt(2)

Then f(8)

f(8) = 8^2 +2/sqrt{8} = 64 + 2 / sqrt(4)sqrt(2) = 64+ 2/2sqrt(2) = 64 + 1/ sqrt(2)

2f(2) - f(8).

2 * (4 + 2/ sqrt(2)) - (64 + 1/ sqrt(2))

8 + 4/ sqrt(2)  - 64 - 1/ sqrt(2)

Combine like terms

-56 +  3 / sqrt(2)

Rationalizing the second term

-56 + 3/ sqrt(2) * sqrt(2)/sqrt(2)

-56 + 3 sqrt(2) /2