Math Problem Statement
Which of the following is the inverse of y = (x - 3)^3?
Solution
To find the inverse of the function , we will follow the steps for determining the inverse of a function:
Step 1: Start with the given function:
Step 2: Swap and :
The inverse function is obtained by switching and :
Step 3: Solve for :
To solve for , take the cube root of both sides:
Now, add 3 to both sides:
Thus, the inverse function is:
Step 4: Identify the correct option:
The correct answer is option D:
Would you like further details on the process or have any questions? Here are 5 related questions to deepen your understanding:
- What is the definition of an inverse function?
- How can you verify that two functions are inverses of each other?
- What is the domain and range of the function ?
- How does the cube root function differ from the square root function in terms of solving for ?
- What happens to the graph of a function when you take its inverse?
Tip: Always remember to swap and when finding the inverse of a function, and then solve for .
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Math Problem Analysis
Mathematical Concepts
Inverse Functions
Cubic Functions
Algebra
Formulas
y = (x - 3)^3
y = cube root of x + 3
Theorems
Inverse Function Theorem
Suitable Grade Level
Grades 10-12