# SOLUTION: Give the domain of the variable in each expression: a. 5 ----- 2n + 3 b. 5n + 1 ------ 7 c. 5n + 1 ------- 7(2n +

Algebra ->  -> SOLUTION: Give the domain of the variable in each expression: a. 5 ----- 2n + 3 b. 5n + 1 ------ 7 c. 5n + 1 ------- 7(2n +       Log On

 Ad: Mathway solves algebra homework problems with step-by-step help! Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!

 Click here to see ALL problems on Functions Question 171810This question is from textbook : Give the domain of the variable in each expression: a. 5 ----- 2n + 3 b. 5n + 1 ------ 7 c. 5n + 1 ------- 7(2n + 3)This question is from textbook Answer by jim_thompson5910(29613)   (Show Source): You can put this solution on YOUR website!I'll do the first two to get you going in the right direction. a) Start with the given expression Set the denominator equal to zero. Remember, dividing by 0 is undefined. So if we find values of n that make the denominator zero, then we must exclude them from the domain. Subtract 3 from both sides Combine like terms on the right side Divide both sides by 2 to isolate n Reduce Since makes the denominator equal to zero, this means we must exclude from our domain So our domain is: which in plain English reads: n is the set of all real numbers except n CANNOT equal So our domain looks like this in interval notation note: remember, the parenthesis excludes -3/2 from the domain b) Looking at , we can see that there are no square roots, logs, and other functions where there are restrictions on the domain. Also, we can see that the function does not have a division by n (or any combination of variables and constants). So we don't have to worry about division by zero. Since we don't have any restrictions on the domain, this shows us that the domain is all real numbers. In other words, we can plug in any number in for n So the domain of the function in set-builder notation is: In plain English, this reads: n is the set of all real numbers (In other words, n can be any number) Also, in interval notation, the domain is: