QuestionUse the definition of a one-to-one function to determine if the function is one-to-one. The function is one-to-one. The function is not one-to-one.
Studdy Solution
STEP 1
1. A function is one-to-one (injective) if every element of the function's domain maps to a unique element in the function's codomain.
2. To determine if a function is one-to-one, we can use the horizontal line test or show that if , then .
STEP 2
1. Understand the definition of a one-to-one function.
2. Apply the definition to the given function .
3. Determine if the function is one-to-one.
STEP 3
Understand the definition of a one-to-one function. A function is one-to-one if for every pair of different inputs, the outputs are different. Mathematically, this means if , then .
STEP 4
Apply the definition to the given function . Assume and show that this implies .
Set them equal:
STEP 5
Simplify the equation by adding 16 to both sides:
Take the cube root of both sides:
This shows that if , then .
STEP 6
Since we have shown that if , then , the function is one-to-one.
The function is one-to-one.
The function is one-to-one.
Was this helpful?