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

Apr 10, 2017

Please verify my solution. Need some guideline to complete.

#### Explanation:

The domain of the given function is the set of $x$ values such that $\sqrt{5 x - {x}^{2} - 6} > 0$

The discriminant of the quadratic equation is:
${\left(5\right)}^{2} - 4 \left(- 1\right) \left(- 6\right) = 1$

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

$x = - b \pm \frac{\sqrt{{b}^{2} - 4 a c}}{2} a$
Putting value of $a = - 1 , b = 5 , c = - 6$ we get:
$x = 2 , 3$