Find the domain of the function $f$ $f$ defined by $f (x) = \frac{1}{\sqrt{5 x - x^{2} - 6}}$ $f(x) = 1/sqrt(5x-x^2-6)$ ?

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Answer 1 · 2017-04-10T21:14:30

Please verify my solution. Need some guideline to complete.

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

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

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

Applying quadratic formula we get:
$x = - b \pm \frac{\sqrt{b^{2} - 4 a c}}{2} a$ $x = -b+-sqrt(b^2-4ac)/2a$

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

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 ?

Find the domain of the function ff defined by f(x)=1√5x−x2−6f(x) = 1/sqrt(5x-x^2-6)?