Question

Which of the following statements is true for inverse functions Æ’(x) and g(x)?

1) (Æ’ ° g)(x) = (g ° Æ’)(x) = x
2) (Æ’ ° g)(x) = (g ° Æ’)(x) = 0
3) (Æ’ ° g)(x) = (g ° Æ’)(x) = 1
4) (Æ’ ° g)(x) = (g ° Æ’)(x) = Æ’(x)

Answer 1

The true statement for inverse functions f(x) and g(x) is that the composition (f composed with g)(x) = (g composed with f)(x) returns the original input x. the first option: (f ∘ g)(x) = (g ∘ f)(x) = x.

Step-by-step explanation:

The true statement for inverse functions f(x) and g(x) is the first option: (f ∘ g)(x) = (g ∘ f)(x) = x. Inverse functions are two functions that 'undo' each other. When one function is applied and then the other is applied to its result, the original input is retrieved. This means that the composition of a function and its inverse yields the identity function, which returns the original input for each element of the function's domain. For example, if f(x) is a function that squares a number and g(x) is its inverse function that takes the square root of a number, then applying g(f(x)) or f(g(x)) to any positive number x will result in the original number x.