#1 Given f(x)-x^2-4 and g(x)=2x-1 how would you determine the value of (f+g)(3) and (f/g)(-1)?



#2 If f(x)=x+2 and g(x)=x how would you find the value or values for which (fg)(x)=8?


Thank you.

We're talking combinations of functions here. It is important to note that (f+g)(x) can also be written as f(x)+g(x). Also, (f/g)(x) = f(x)/g(x), and similarly, (fg)(x) = f(x)g(x).

So, for #1, simply write out what (f+g)(x) is, and then evaluate for x=3 (ie, replace every x in the equation with the number 3). Do the same for (f/g)(x), and evaluate for x=-1.

For #2, write out what (fg)(x) is. Then, set that equal to 8. Move the eight over to the other side of the equation, and you will have a nice, familiar polynomial of the 2nd degree to factor.