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

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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 $x$ 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 ?

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