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Question 20373: For f(x)= 2x-5 and g(x)= 3-x , find (f (times) g)(-2)
Answer by longjonsilver(2297)   (Show Source):
You can put this solution on YOUR website! 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.
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