Answer :
a)
f(x) = {(a , 8) , (b , 2) , (c , 14) , (d , 12) , (e , 6)}
The domain of f(x) is {a, b , c , d , e}
The output of f(x) is {8 , 2 , 14 , 12 , 6}
b)
g(x) = {(8 , a) , (2 , b) , (14 , c) , (12 , d) , (6 , e)}
Step-by-step explanation:
Let us revise the composite function
- A composite function is created when one function is substituted into another function
- (f ο g)(x) is the composite function that is formed when g(x) is substituted for x in f(x)
- If (f ο g)(x) = (g ο f)(x) = x, then g(x) if the inverse of f(x) and vice versa
A = {a, b, c, d, e} and B = {2, 4, 6, 8, 10, 12, 14}
a)
∵ f(a) = 8, f(b) = 2, f(c) = 14, f(d) = 12, f(e) = 6
∴ f(x) = {(a , 8) , (b , 2) , (c , 14) , (d , 12) , (e , 6)}
- The domain of f(x) is the set of x-coordinates of the ordered
pairs and the output is the set of y-coordinates of the ordered
pairs
∴ The domain of f(x) is {a, b , c , d , e}
∴ The output of f(x) is {8 , 2 , 14 , 12 , 6}
f(x) = {(a , 8) , (b , 2) , (c , 14) , (d , 12) , (e , 6)}
The domain of f(x) is {a, b , c , d , e}
The output of f(x) is {8 , 2 , 14 , 12 , 6}
b)
∵ The domain of g(x) is in B
∵ The output of g(x) is in A
∵ (g ◦ f)(x) = x for all x ∈ A
- When (g ο f)(x) = x, then g(x) if the inverse function of f(x)
∴ g(x) is the inverse of f(x)
∵ If function g is the inverse of a function f where y = f(x) then x = g(y)
- That means switch the coordinates of the ordered pairs of f(x)
to get g(x)
∴ g(8) = a , g(2) = b , g(14) = c , g(12) = d , g(6) = e
∴ g(x) = {(8 , a) , (2 , b) , (14 , c) , (12 , d) , (6 , e)}
g(x) = {(8 , a) , (2 , b) , (14 , c) , (12 , d) , (6 , e)}
Learn more:
You can learn more about the functions in brainly.com/question/10382722
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