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What is a A relationship that assigns exactly one output value to one input value?
It is a injective relationship. However, it need not be surjective and so will not be bijective. It will, therefore, not define an invertible function.
What are some function words?
Domain, codomain, range, surjective, bijective, invertible, monotonic, continuous, differentiable.
Prove that the inverse of an invertible mapping is invertible?
Assume that f:S->T is invertible with inverse g:T->S, then by definition of invertible mappings f*g=i(S) and g*f=i(T), which defines f as the inverse of g. So g is invertible.
Is a to power of 4 multiplied by b to power of 5 invertible?
Indeterminate. How? a4b5 is the expression instead of equality. Since we are not given the equality of two variables, there is no way to determine whether it's invertible or not. Otherwise, if you are referring "a" and "b" as invertible matrices, then yes it's invertible. This all depends on the details.
What is the opposite integer of 1?
The answer depends on the context for opposite. Common opposites are the additive or multiplicative inverses but any invertible function can be used to define an opposite.
