Option first, and option second represent the function; f(x) and g(x) are inverses of each other option first, and option second are correct.
<h3>What is a function?</h3>
It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have a shown function in the picture.
As we know if the function f(x) has double ordered (x, y) that satisfies the function.
Then it's inverse of a function g(x) must have ordered pair (y, x)
f(x) = {(-5,-9), (-3, -4), (0, 1), (3, 7), (6, 13)}
g(x) = {(-9,-5), (-4,-3), (1, 0), (7,3), (13,6)}
As we can see in the f(x) and g(x) they both have ordered pair (x, y) in f(x) and (y, x) in the g(x).
The f(x) and g(x) are inverses of each other.
f(x) = x + 7
g(x) = x - 7
To find the inverse of f(x)
Interchange the value of f(x) and x
x → g(x)
f(x) → x
x = g(x) + 7
g(x) = x -7
The f(x) and g(x) are inverses of each other.
The table does not represent any relation that shows that the f(x) and g(x) are inverses of each other.
Thus, option first, and option second represent the function; f(x) and g(x) are inverses of each other option first, and option second are correct.
Learn more about the function here:
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