Express g(f(x)) and f(g(x)), if they exist, as sets of ordered pairs.
f= {(3,8),(2,5),(4,-5),(9,3)}
g= {(9,2),(-5,3),(5,9),(8,10),(1,9)}
g(f(x)) = {g(8),g(5),g(-5),g(3)}
= {10,9,3}
g(3) is undefined
To express g(f(x)) and f(g(x)) as sets of ordered pairs, we need to perform the compositions of the two functions.
To find g(f(x)), we need to evaluate f(x) first and then use the output as the input for g(x).
f(x) maps each input to its corresponding output in the function f:
f = {(3,8),(2,5),(4,-5),(9,3)}
Let's evaluate f(x) using some input values:
f(3) = 8
f(2) = 5
f(4) = -5
f(9) = 3
Now, we can use these outputs as inputs for g(x):
g = {(9,2),(-5,3),(5,9),(8,10),(1,9)}
g(8) = 10
g(5) = 9
g(-5) = 3
g(9) = 2
Now, we can express g(f(x)) as a set of ordered pairs:
g(f(x)) = {(3,10),(2,9),(4,3),(9,2)}
To find f(g(x)), we need to evaluate g(x) first and then use the output as the input for f(x).
g(x) maps each input to its corresponding output in the function g:
g = {(9,2),(-5,3),(5,9),(8,10),(1,9)}
Let's evaluate g(x) using some input values:
g(9) = 2
g(-5) = 3
g(5) = 9
g(8) = 10
Now, we can use these outputs as inputs for f(x):
f = {(3,8),(2,5),(4,-5),(9,3)}
f(2) = 5
f(3) = 8
f(9) = 3
f(10) = (Undefined)
It's important to note that f(10) does not have an output in the given function f. Thus, f(g(x)) cannot be defined as a set of ordered pairs.
To summarize:
g(f(x)) = {(3,10),(2,9),(4,3),(9,2)}
f(g(x)) is undefined as a set of ordered pairs.