What is the domain of h(x)= 1/(4x^2 -21x -18)

In general as we know fraction is define for all number only there is one condition that denominator can not be equal to zero.

So let's find first where denominator is equal to zero.

For that we can solve


Now we can solve it by factoring.

As we know -18 * 4 = -72

So we have to break -72 in such two parts whose summation equal to -21x and multiplication equal to -72.

So we can write -72 as = -24 * 3

Because when we add -24 and 3 we will get -21

So we can write equation as




SO we can say x = 6 or x =

So we can say our fraction is define for all real number but x can not be equal to 6 or because at these values denominator is zero.

SO domain is set of all real number expect x = 6 or

both graphs increase on their domain

neither graph has a y-intercept

step-by-step explanation:

the following points can be visualized easily from the graph

there is a hike in both the graphs so the graphs are increasing on their domain.x-intercept of log x and log 6x are differentthere is a vertical asymptote of both the graphs so there is no y-interceptas both the graphs are increasing so there is no horizontal asymptote