Question 1173960: If f = {(-2,5),(1,4),(3,9),(11,3)} and g = {(0,15),(5,-5),(7,10),(9,-1), what is (g o f)(3)?
Answer by math_tutor2020(3816)   (Show Source):
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The notation (g o f)(3) is equivalent to g(f(3))
You keep the letters in the same order. In this case, g is to the left of f.
With g(f(3)), we see that f(3) is the inner function we need to compute first
The function f(x) given to us is
f = {(-2,5),(1,4),(3,9),(11,3)}
From this, we look where x = 3. That would be the point (3,9)
So f(3) = 9
We could say that when x = 3, we have y = f(x) = 9
Any of those points listed is in the form (x,y)
With that in mind, g(f(3)) updates to g(9)
I've replaced f(3) with 9 since f(3) = 9, ie, f(3) and 9 are the same number.
Now we follow the same idea for g(x). We look for the point when x = 9
g = {(0,15),(5,-5),(7,10),(9,-1)}
That point is (x,y) = (9,-1)
So x = 9 and y = f(x) = -1 pair up together.
This makes g(9) = -1
To summarize:
(g o f)(3) is the same as g(f(3))
f(3) = 9, so g(f(3)) becomes g(9)
g(9) = -1
Overall,
g(f(3)) = -1
which converts to the notation
(g o f)(3) = -1
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Answer: -1
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