Consider the following equations

Question

f(x)=1/x, g(x)=3/x+3

Find (f + g)(x).

 

Find the domain of (f + g)(x).

 (Enter your answer using interval notation.)

 

Find (f − g)(x).

 

Find the domain of (f − g)(x).

 (Enter your answer using interval notation.)

 

Find (fg)(x).

 

Find the domain of (fg)(x).

 (Enter your answer using interval notation.)

 

Find (f/g)(x)

Find the domain of (f/g)(x). (Enter your answer using interval notation.)

Answer 1

Hi Simon G.

I don't understand what difficulty you are having with these problems. All of these are just "plug-in and crank" type calculations. Plug in each function expression, and combine them just as the problem indicates: sum, difference, product, and quotient respectively.

You may need to convert mixed expressions into standard form, with common denominators -- that's not a problem, is it?

For the domain and range bits, domain checking just means that you make sure that you "cut-out" ANY x values that cause a division by zero (or any other forbidden operation, such as taking the square root of a negative number). So if the denominator of a term is x, then x=0 is forbidden (the domain is an open interval on either side of that point, but the point itself is excluded).

You may also find it necessary to break your domain up into pieces, bounded by all of those breaks in the domain. Why? Because the calculated expression for the range value is likely to flip sign at those points, and therefore you MAY need different expressions or calculations to take that into account. So you may need different pieces of algebraic expressions for the range for EACH of the domain pieces you have.

-- Cheers, -- Mr. d.