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Numerade Educator

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Problem 52 Hard Difficulty

Use the table to evaluate each expression.

(a) $ f (g(1)) $
(b) $ g (f(1)) $
(c) $ f (f(1)) $
(d) $ g (g(1)) $
(e) $ (g \circ f) (3) $
(f) $ (f \circ g) (6) $

Answer

a) $f(g(1))=5$
b) $g(f(1))=2$
c) $f(f(1))=4$
d) $g(g(1))=3$
e) $(g \circ f)(3)=1$
f) $(f \circ g)(6)=4$

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Video Transcript

Let's use the table to find f of G of one. So first we're going to find G of one. So we used the G row and the one column, and we find that g of oneness. Six. So let's replace GF one with six, and now we're looking for F of six. So let's use the six column and the F row and F of six is five. So the answer is that Now let's find G of f of one. So first, let's find f of one. So we use the one column and the F ro and we get f of one is three. So now we're looking for G of three. So we used the three column and the G Row and G of three is, too. So your answer is to now for part C. Let's find af f of one. So we start by finding f of one. So we use the one row for the one column and the F row and 1/2 of one is three. So we substitute that in, and now we're finding f of three. So to find f of three, we used the F ro and the three column and we get F of three is four. So the answer is for now, let's find G of G of one. So starting with the inside g of one, we use the one column and the G row, and we get six g of 1 to 6. So we substitute that in, and now we're finding G of six. So we use the six column and the G Row and G of sixes three. So our answer is three. Next for party. Let's find G of F of three and another way to write. That would be G of f of three just with parentheses like that. So let's start by finding f of three. So we used the three column and the F Row F of three is four. So we substitute that in, and now we're finding Geo for So use the four column and the G Row G affords one. So our answer is one. Now let's do part F, and we could write Rewrite this as f of G of six with parentheses like so? So we'll start on the inside and find G of six. So we use the six column and the G Row G of six is three, So we'll substitute that in and we have f of three. So now we're going to use the three column and the F Row F of three is four. So our answer is for