Calculus 3 Review

Question

If 

Find f(x) and F(4)

Answer 1

f(x) = sqr(x-3)/sqr(x+3) = sqr((x-3)/(x+3))

maybe you meant f(x) = (sqrx -3)/(sqrx + 3)

then rationalize the denominator by multiplying by the conjugate of the denominator: (sqrx-3)/(sqrx+3) times (sqrx-3)/(sqrx-3) = (x -6sqrx +9)/(x -9)

UNLESS you more likely meant:

f(x) = sqrx - 3/sqrx + 3 = x/sqrx -3/sqrx + 3sqrx/sqrx = (x-3+3sqrx)/sqrx

F(x) generally means the integral of f(x)

F(x) = x^3/2/(3/2) - 3x^1/2/(1/2) + 3x + c where c = a constant

F(x) = (2/3)x^3/2 -6x^1/2 + 3x + c

F(4) = (2/3)8 - 6(2) +3(4) + c

= 16/3 + c

UNLESS you meant the 1st or 2nd version, which seems more unlikely, then F(x) and F(4) are different