In mathematics, two functions, f and g, can be said to be inverses if they have the property that when one of them is applied to a certain number or value, the other function will produce the same number. For example, if we apply f(x) = -x + 2 to any given x-value then applying g(x) = -x + 6 afterwards will result in obtaining back our original x-value again. Therefore, for these two functions to be inverse of each other their composition must equal the identity function i.e., (f ∘ g)(x) = (g ∘ f)(x) = x.

To determine whether two functions are inverse of each other we need to first understand what composition means and how it works with respect to these two functions; f and g. Composition essentially refers to combining multiple mathematical operations or computations into one single operation or computation using a process known as ‘chaining’. In this particular case chaining entails creating a new function h(x) which is created by assigning f as the input parameter for g such that: h(x)=g(-x+2). The resulting equation would look like this: h(x)= -(-x+2)+6= x+4 so h(X)=X+4 ; This implies that when we plug in any value/number into either side of this equation we’ll get back our original number unchanged – making them an inverse pair.

See also  Prove that the union of two denumerable sets is denumerable. Proof that the Union of Two Denumerable Sets is Denumerable