Question

Determine the domain of (f/g)(x) when f (x)=1/x and g (x)=sqrtx+5

Answer 1

we are given

`f(x)=(1)/(x)`

`g(x)=√(x+5)`

Calculation of (f/g)(x):

`((f)/(g))(x)=(f(x))/(g(x))`

now, we can plug values

`((f)/(g))(x)=((1)/(x))/(√(x+5))`

now, we can simplify it

`((f)/(g))(x)=(1)/(x√(x+5))`

Domain:

we know that domain is all possible values of x for which any function is defined

function will be undefined when denominator =0

`x√(x+5) =0`

`x=-5,x=0`

we are given sqrt function

and we know that value inside sqrt will always be greater than 0

`x+5>0`

`x>-5`

so, domain will be

`(-5,0)U(0,\infty)`..............Answer