Inverses of Quadratics and Roots

Front

What is the inverse of a function?

Back

The inverse of a function is obtained by switching the x's and y's in the function's equation.

Front

How do you find the inverse of the function f(x) = √x - 6?

Back

To find the inverse, set y = √x - 6, switch x and y, and solve for y: y = (x + 6)².

Front

What is the inverse of the function y = √(x + 11)?

Back

The inverse is found by switching x and y, resulting in y = x² - 11.

Front

What is the inverse of the function y = (x - 4)² + 3?

Back

The inverse is y = √(x - 3) + 4.

Front

What is the significance of the vertex in a quadratic function?

Back

The vertex is the highest or lowest point of the parabola, depending on its orientation.

Front

What does it mean for a function to be one-to-one?

Back

A function is one-to-one if each output is produced by exactly one input, allowing for an inverse to exist.

Front

How can you determine if a function has an inverse?

Back

A function has an inverse if it is one-to-one, which can be tested using the horizontal line test.

Front

What is the relationship between a function and its inverse?

Back

The inverse function reverses the effect of the original function; if f(a) = b, then f⁻¹(b) = a.

Front

What is the domain of the inverse function of y = √(x + 11)?

Back

The domain of the inverse function is the range of the original function, which is [11, ∞).

Front

What is the range of the inverse function of y = (x - 4)² + 3?

Back

The range of the inverse function is the domain of the original function, which is [3, ∞).