Question

Find the domain of the function `f` defined by `f(x) = 1/sqrt(5x-x^2-6)`?

Answer 1

Please verify my solution. Need some guideline to complete.

Explanation:

The domain of the given function is the set of `x` values such that `sqrt(5x-x^2-6) > 0`

The discriminant of the quadratic equation is:
`(5)^2-4(-1)(-6) = 1`

Since the discriminant is positive the equation has two real number value of `x`

Applying quadratic formula we get:
`x = -b+-sqrt(b^2-4ac)/2a`

Putting value of `a=-1, b=5, c= -6` we get:
`x=2,3`

Now with the values 2 and 3 the above function becomes undefined, so that with any real numbers.

How should I proceed next.... any help ?