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Yes, a function needs to be one-to-one in order to have an inverse.
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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.
What is the relation in which each element in the domain is mapped to exactly one element the range?
It is an invertible function.
Can an invertible function have more than one x-intercept?
No. If the function has more than one x-intercept then there are more than one values of x for which y = 0. This means that, for the inverse function, y = 0 should be mapped onto more than one x values. That is, the inverse function would be many-to-one. But a function cannot be many-to-one. So the "inverse" is not a function. And tat means the original function is not invertible.
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 is an input or output relation that has exactly one output for each input?
A one-to-one function, a.k.a. an injective function.
What rule assigns each value of the independent variable to exactly one value of the dependent variable?
It is any invertible function.
If matrix a is invertible and a b is invertible and a 2b a 3b and a 4b are all invertible how can you prove that a 5b is also invertible?
What is "a 3b"? Is it a3b? or a+3b? 3ab? I think "a3b" is the following: A is an invertible matrix as is B, we also have that the matrices AB, A2B, A3B and A4B are all invertible, prove A5B is invertible. The problem is the sum of invertible matrices may not be invertible. Consider using the characteristic poly?
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.
What are some examples for a function word?
Here are some examples:Domain, codomain, range, surjective, bijective, invertible, monotonic, continuous, differentiable.
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.
What is invertible counterpoint?
Invertible counterpoint The contrapuntal design of two or more voices in a polyphonic texture so that any of them may serve as an upper voice or as the bass. Invertible counterpoint involving two (three, four) voices is called double (triple, quadruple) counterpoint. http://www.answers.com/topic/invertible-counterpoint-music
