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

we are given

Calculation of (f/g)(x):

now, we can plug values

now, we can simplify it

Domain:

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

function will be undefined when denominator =0

we are given sqrt function

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

so, domain will be

..............Answer

d is correct

step-by-step explanation:

so, converting firstly the mixed fractions to improper fractions and then "adding".