Given the functions f(x)=3x-2-4/x, and g(x)=2-3x, find the indicated values: f(a+b) and g(a)-g(a-b)+f(a)
So these may seem hard because your dealing with a bunch of variables but they are fairly simple once you understand that you can treat the variables a and b just like x (or y or any other letter). For f(a+b) you are replacing x with a+b, or use the equation x=a+b. f(a+b)=3(a+b)-2-4/(a+b). Now simplify like any other equation. The 3(a+b) separate using distributive property, but won't seperate on the4/(a+b) (since the a=b is on the denominator). We would get f(a+b)=3a+3b-2-4/(a+b). Now to show this you don't need to write out a paragraph, instead show all the steps in order and your teacher should be able to see how you did it.
For g(a)-g(a-b)+f(a) its going to be a little harder. You can solve it just like above and you would get the same answer, but I know a faster way. First notice what type of function g(x) is. Go check it out now. Okay its linear (aka a line). Lines behave differently in these situations. They are distributive. Essentially g(a+b)=g(a)+g(b). This means we can simplify the equation without plugging in the variables like before. g(a)-g(a-b)+f(a)=g(a)-g(a)-[-g(b)]+f(a)=g(b)+f(a). Now solve g(b)+f(a) like above. Now if you are wondering why f(a) can't be simplified out its because it is non-linear so it cant be added. You can only distribute or condense equations of the form y=mx+b and only if they are the same m and b. The 4/x makes it non linear. You should be able to solve the second one on your own now, but if you have any questions please ask me.