Question 20373
i assume your f times g means fg(x).


This means do the g(x) function first, and then that answer is put into the function f.


We can do this step by step as follows:


g(x) = 3-x, so g(-2) becomes 3-(-2) --> 3+2 --> 5
so, g(-2) = +5


Now we put this answer into f, where f(x) = 2x-5. This then becomes f(5) = 2(5)-5


--> f(5) = 10-5
--> f(5) = 5


So fg(-2) = 5


Alternative method (so you can see) is to combine the 2 functions first, before putting the value -2 into it:


fg(x) = f(3-x). Now we put (3-x) into the f function.


Since f(x) = 2x-5, we get
f(3-x) = 2(3-x) - 5
f(3-x) = 6-2x -5
f(3-x) = 1-2x


so, together, fg(x) = 1-2x


Now, fg(-2) = 1-2(-2)
--> 1+4
--> 5


I hope this is clearer for you. Look at my Lesson on Functions on the website, too.


jon.