Find the inverse of f(x)=3x^2-3x-11

Question

The answer key states that the answer is

(1/2 ) + √(x/3) + (47/12), but i got (1/2) + √[(x/3)+(47/12)]. I would like to know where I gone wrong.

Thank you for your help!

Answer 1

y=3x^2 -3x -11

switch x and y

x = 3y^2 -3y -11

solve for y

y = 3/6 +/- (1/6)sqr(9 - 4(3)(-11-x)

f^-1(x)= the inverse relation = .5+ or - (1/6)sqr(141 +12x)