True or False?

Question

For x is greater than or equal to -b/2a,
the inverse of the function f(x) = ax^2 + bx + c is the function
g(x) = {-b + the square root of *[(b^2 - 4a(c - x))]*} / 2a
provided that 4ax + b^2 - 4ac is greater than or equal to 0.

Answer 1

True.

The inverse function is what you get when you interchange the x and the y. You did this and then used the general solution for a quadratic.

Check:
If you substitute the inverse function in for x then you should end up with just x.

x^2 = (b^2 - 2bSQRT(b^2 - 4a(c - x)) + b^2 - 4a(c - x)))/4a^2
x^2 = b^2/(2a^2) - (b/(2a2))SQRT(b^2 - 4a(c - x)) - (c - x)/a
ax^2 = b^2/(2a) - (b/2a)SQRT(b^2 - 4a(c - x)) - (c - x)

bx = (-b^2 + bSQRT(b^2 - 4a(c - x)))/2a
bx = b^2/(2a) - (b/2a)SQRT(b^2 - 4a(c - x))

Put this all together and you get:

a^2 + b^x + c = x
Therefore g(x) is the inverse of f(x)

Answer 2

AS FAR AS I AM CONCERNED THE GIVEN STATEMENT IS FALSE