Answer: The answer is (d) f(g(x)) = x and g(f(x)) = x.
Step-by-step explanation: We are to select the correct statement that verifies the functions f(x) and g(x) are inverses of each other.
We know that if f(x) is the inverse of g(x), then we write
[tex]g^{-1}(x)=f(x)~~~\Rightarrow g(f(x))=x.[/tex]
If g(x) is the inverse of f(x), then we write
[tex]f^{-1}(x)=g(x)~~~\Rightarrow f(g(x))=x.[/tex]
So, we can write
f(g(x)) = x and g(f(x)) = x.
Thus, the correct option is (d).
By definition, we will see that the correct option is:
"f(g(x)) = x and g(f(x)) = x"
Two functions are inverses of each other when the composition of these functions (in any order) is equal to the identity function. This means, that the output of the composition must be equal to the input p.
If we define:
f(x) and g(x) are only inverses if:
H(x) = x = K(x)
which means that:
f(g(x)) = x = g(f(x))
Then the correct option is the last one:
"f(g(x)) = x and g(f(x)) = x"
If you want to learn more about inverse functions, you can read:
https://brainly.com/question/12220962