Which equation can be simplified to find the inverse of y = 5x² + 10?
Answer: x = 5y² + 10 can be simplified to find the inverse of y = 5x² + 10
In mathematics, finding the inverse of a function involves switching the roles of the input (x) and output (y) and solving for the new output in terms of the input. This process is especially important for functions to determine if their inverse is also a function, and to understand the relationship between the two. For the function y = 5x² + 10, finding its inverse requires algebraic manipulation.
Methods
Math Tutor Explanation Using the Variable Switching Method
Here we'll swap x and y positions in the original equation, and then solve for y.
Step 1: Step 1: Rewrite y = 5x² + 10 as x = 5y² + 10 by switching x and y
Step 2: Step 2: Solve the equation x = 5y² + 10 for y to get the inverse
Math Tutor Explanation Using Inverse Function Steps
These are the general steps for finding an inverse for a function.
Step 1: Step 1: Replace y with f(x) to make notation clearer (let y = 5x² + 10)
Step 2: Step 2: Swap x and y (get x = 5y² + 10)
Math Tutor suggests: Strengthen Your Understanding of Function Inverses and Quadratic Equations
Explore more examples and concepts related to inverting functions, quadratic equations, and related algebra skills with these recommended questions.
FAQ on Finding Inverses of Quadratic Functions
Can all quadratic functions be inverted?
Not always; quadratics are not one-to-one unless their domain is restricted.
Why do we switch x and y to find an inverse?
Switching the variables reflects the function across the line y=x, revealing the inverse relationship.
What is the inverse of y = 5x² + 10?
After switching and solving, the inverse can be written as y = ±sqrt((x-10)/5).
Is the inverse of a quadratic always a function?
No, the inverse of a general quadratic is not a function unless we restrict the domain.
- Answer: x = 5y² + 10 can be simplified to find the inverse of y = 5x² + 10
- Methods
- Math Tutor Explanation Using the Variable Switching Method
- Math Tutor Explanation Using Inverse Function Steps
- Math Tutor suggests: Strengthen Your Understanding of Function Inverses and Quadratic Equations
- FAQ on Finding Inverses of Quadratic Functions
- Can all quadratic functions be inverted?
- Why do we switch x and y to find an inverse?
- What is the inverse of y = 5x² + 10?
- Is the inverse of a quadratic always a function?
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