Finite Math Examples

Determine if Injective (One to One)
Function is said to be injective or one-to-one if every element in the range is an image of at most one element from the domain.
An injective function is called a one-to-one function
Since is on the right side of the equation, switch the sides so it is on the left side of the equation.
Move to the left side of the equation by subtracting it from both sides.
Use the quadratic formula to find the solutions.
Substitute the values , , and into the quadratic formula and solve for .
Simplify.
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Simplify the numerator.
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Raise to the power of to get .
Multiply by to get .
Multiply by to get .
Multiply by to get .
Multiply by to get .
Factor out of .
Simplify the denominator.
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Rewrite.
Multiply by to get .
Simplify .
Simplify the expression to solve for the portion of the .
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Simplify the numerator.
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Raise to the power of to get .
Multiply by to get .
Multiply by to get .
Multiply by to get .
Multiply by to get .
Factor out of .
Simplify the denominator.
Tap for more steps...
Rewrite.
Multiply by to get .
Simplify .
-----Begin simplification-----
Simplify the expression to solve for the portion of the .
Tap for more steps...
Simplify the numerator.
Tap for more steps...
Raise to the power of to get .
Multiply by to get .
Multiply by to get .
Multiply by to get .
Multiply by to get .
Factor out of .
Simplify the denominator.
Tap for more steps...
Rewrite.
Multiply by to get .
Simplify .
-----Begin simplification-----
The final answer is the combination of both solutions.
There is more than value for some values, which means that is not an equation of a function.
Not Injective (Not One-to-One)
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